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Your data matches 124 different statistics following compositions of up to 3 maps.
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Matching statistic: St001880
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Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00252: Permutations —restriction⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[+,+,+,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,+,+,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,-,+,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,+,-,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,+,+,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,-,+,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,+,-,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,+,+,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,-,-,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,-,+,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,+,-,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,-,-,+] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,-,+,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,+,-,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,-,-,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,-,-,-] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,+,4,3] => [1,2,4,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,+,4,3] => [1,2,4,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,-,4,3] => [1,2,4,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,-,4,3] => [1,2,4,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,4,2,3] => [1,4,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[-,4,2,3] => [1,4,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[4,1,2,3] => [4,1,2,3] => [1,2,3] => ([(0,2),(2,1)],3)
=> 3
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,-,-,+,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,-,+,-,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
[-,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St000924
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
St000924: Perfect matchings ⟶ ℤResult quality: 65% ●values known / values provided: 65%●distinct values known / distinct values provided: 75%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
St000924: Perfect matchings ⟶ ℤResult quality: 65% ●values known / values provided: 65%●distinct values known / distinct values provided: 75%
Values
[+,+,+,+] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[-,+,+,+] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[+,-,+,+] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[+,+,-,+] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[+,+,+,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[-,-,+,+] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[-,+,-,+] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[-,+,+,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[+,-,-,+] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[+,-,+,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[+,+,-,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[-,-,-,+] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[-,-,+,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[-,+,-,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[+,-,-,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[-,-,-,-] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> 4 = 3 + 1
[+,+,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> 4 = 3 + 1
[-,+,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> 4 = 3 + 1
[+,-,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> 4 = 3 + 1
[-,-,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> 4 = 3 + 1
[+,4,2,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> 4 = 3 + 1
[-,4,2,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> 4 = 3 + 1
[4,1,2,3] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
=> [(1,8),(2,7),(3,6),(4,5)]
=> 4 = 3 + 1
[+,+,+,+,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,+,+,+,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,-,+,+,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,+,-,+,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,+,+,-,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,+,+,+,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,-,+,+,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,+,-,+,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,+,+,-,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,+,+,+,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,-,-,+,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,-,+,-,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,-,+,+,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,+,-,-,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,+,-,+,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,+,+,-,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,-,-,+,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,-,+,-,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,-,+,+,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,+,-,-,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,+,-,+,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,+,+,-,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,-,-,-,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,-,-,+,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,-,+,-,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,+,-,-,-] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[-,-,-,-,+] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> 5 = 4 + 1
[+,3,2,+,+,+] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[-,3,2,+,+,+] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[+,3,2,-,+,+] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[+,3,2,+,-,+] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[+,3,2,+,+,-] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[-,3,2,-,+,+] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[-,3,2,+,-,+] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[-,3,2,+,+,-] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[+,3,2,-,-,+] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[+,3,2,-,+,-] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[+,3,2,+,-,-] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[-,3,2,-,-,+] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[-,3,2,-,+,-] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[-,3,2,+,-,-] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[+,3,2,-,-,-] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[-,3,2,-,-,-] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> ? = 5 + 1
[+,3,2,+,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]
=> ? = 5 + 1
[-,3,2,+,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]
=> ? = 5 + 1
[+,3,2,-,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]
=> ? = 5 + 1
[-,3,2,-,6,5] => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]
=> ? = 5 + 1
[+,3,2,6,4,5] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]
=> ? = 5 + 1
[-,3,2,6,4,5] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
=> [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]
=> ? = 5 + 1
[+,3,4,2,+,+] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]
=> ? = 4 + 1
[-,3,4,2,+,+] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]
=> ? = 4 + 1
[+,3,4,2,-,+] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]
=> ? = 4 + 1
[+,3,4,2,+,-] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]
=> ? = 4 + 1
[-,3,4,2,-,+] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]
=> ? = 4 + 1
[-,3,4,2,+,-] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]
=> ? = 4 + 1
[+,3,4,2,-,-] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]
=> ? = 4 + 1
[-,3,4,2,-,-] => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]
=> ? = 4 + 1
[+,3,4,2,6,5] => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]
=> ? = 4 + 1
[-,3,4,2,6,5] => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]
=> ? = 4 + 1
[+,3,4,6,2,5] => [1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0]
=> [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]
=> ? = 4 + 1
[-,3,4,6,2,5] => [1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0]
=> [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]
=> ? = 4 + 1
[+,3,6,2,4,5] => [1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0]
=> [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]
=> ? = 5 + 1
[-,3,6,2,4,5] => [1,3,6,2,4,5] => [1,0,1,1,0,1,1,1,0,0,0,0]
=> [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]
=> ? = 5 + 1
[+,3,6,+,2,5] => [1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0]
=> [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]
=> ? = 4 + 1
[-,3,6,+,2,5] => [1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0]
=> [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]
=> ? = 4 + 1
[+,3,6,-,2,5] => [1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0]
=> [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]
=> ? = 4 + 1
[-,3,6,-,2,5] => [1,3,6,4,2,5] => [1,0,1,1,0,1,1,1,0,0,0,0]
=> [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]
=> ? = 4 + 1
[+,4,2,3,+,+] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]
=> ? = 4 + 1
[-,4,2,3,+,+] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]
=> ? = 4 + 1
[+,4,2,3,-,+] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]
=> ? = 4 + 1
[+,4,2,3,+,-] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]
=> ? = 4 + 1
[-,4,2,3,-,+] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]
=> ? = 4 + 1
[-,4,2,3,+,-] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]
=> ? = 4 + 1
[+,4,2,3,-,-] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]
=> ? = 4 + 1
[-,4,2,3,-,-] => [1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]
=> ? = 4 + 1
[+,4,2,3,6,5] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]
=> ? = 4 + 1
[-,4,2,3,6,5] => [1,4,2,3,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]
=> ? = 4 + 1
Description
The number of topologically connected components of a perfect matching.
For example, the perfect matching $\{\{1,4\},\{2,3\}\}$ has the two connected components $\{1,4\}$ and $\{2,3\}$.
The number of perfect matchings with only one block is [[oeis:A000699]].
Matching statistic: St001879
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 51% ●values known / values provided: 51%●distinct values known / distinct values provided: 75%
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 51% ●values known / values provided: 51%●distinct values known / distinct values provided: 75%
Values
[+,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,+,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,+,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,-,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,-,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[-,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[4,1,2,3] => [4,1,2,3] => [[.,[.,[.,.]]],.]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[+,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,-,+,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,-,-,+,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,-,+,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,-,+,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,-,+,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,+,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,-,-,-] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,-,-,-,+] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,3,2,+,+] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[-,3,2,+,+] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[+,3,2,-,+] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[+,3,2,+,-] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[-,3,2,-,+] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[-,3,2,+,-] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[+,3,2,-,-] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[-,3,2,-,-] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[+,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[-,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[+,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[-,3,5,2,4] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ? = 4
[+,5,+,2,4] => [1,5,3,2,4] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? = 4
[-,5,+,2,4] => [1,5,3,2,4] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? = 4
[+,5,-,2,4] => [1,5,3,2,4] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? = 4
[-,5,-,2,4] => [1,5,3,2,4] => [.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? = 4
[5,1,+,2,4] => [5,1,3,2,4] => [[.,[[.,.],[.,.]]],.]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? = 4
[5,1,-,2,4] => [5,1,3,2,4] => [[.,[[.,.],[.,.]]],.]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ? = 4
[+,+,4,3,+,+] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,+,4,3,+,+] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,-,4,3,+,+] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,+,4,3,-,+] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,+,4,3,+,-] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,-,4,3,+,+] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,+,4,3,-,+] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,+,4,3,+,-] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,-,4,3,-,+] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,-,4,3,+,-] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,+,4,3,-,-] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,-,4,3,-,+] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,-,4,3,+,-] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,+,4,3,-,-] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,-,4,3,-,-] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,-,4,3,-,-] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,+,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,+,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,-,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,-,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,+,4,6,3,5] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,+,4,6,3,5] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,-,4,6,3,5] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[-,-,4,6,3,5] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]]
=> ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
=> ? = 5
[+,+,6,+,3,5] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5
[-,+,6,+,3,5] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5
[+,-,6,+,3,5] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5
[+,+,6,-,3,5] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5
[-,-,6,+,3,5] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5
[-,+,6,-,3,5] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5
[+,-,6,-,3,5] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5
[-,-,6,-,3,5] => [1,2,6,4,3,5] => [.,[.,[[[.,.],[.,.]],.]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Matching statistic: St001875
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001875: Lattices ⟶ ℤResult quality: 41% ●values known / values provided: 41%●distinct values known / distinct values provided: 75%
Mp00065: Permutations —permutation poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
St001875: Lattices ⟶ ℤResult quality: 41% ●values known / values provided: 41%●distinct values known / distinct values provided: 75%
Values
[+,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[-,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[+,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[+,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[+,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[-,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[-,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[-,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[+,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[+,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[+,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[-,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[-,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[-,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[+,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[-,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[+,+,4,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 5 = 3 + 2
[-,+,4,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 5 = 3 + 2
[+,-,4,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 5 = 3 + 2
[-,-,4,3] => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 5 = 3 + 2
[+,4,2,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 5 = 3 + 2
[-,4,2,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 5 = 3 + 2
[4,1,2,3] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 3 + 2
[+,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,-,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,-,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,-,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,+,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,-,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[-,-,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6 = 4 + 2
[+,+,5,3,4] => [1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 4 + 2
[-,+,5,3,4] => [1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 4 + 2
[+,-,5,3,4] => [1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 4 + 2
[-,-,5,3,4] => [1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
=> ? = 4 + 2
[+,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ? = 4 + 2
[-,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ? = 4 + 2
[+,3,5,2,4] => [1,3,5,2,4] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ? = 4 + 2
[-,3,5,2,4] => [1,3,5,2,4] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
=> ? = 4 + 2
[+,5,2,3,4] => [1,5,2,3,4] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? = 4 + 2
[-,5,2,3,4] => [1,5,2,3,4] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
=> ? = 4 + 2
[+,5,+,2,4] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
=> ? = 4 + 2
[-,5,+,2,4] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
=> ? = 4 + 2
[+,5,-,2,4] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
=> ? = 4 + 2
[-,5,-,2,4] => [1,5,3,2,4] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,5),(1,8),(2,7),(2,9),(3,6),(3,9),(4,6),(4,7),(5,2),(5,3),(5,4),(6,10),(7,10),(9,1),(9,10),(10,8)],11)
=> ? = 4 + 2
[5,1,2,3,4] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 4 + 2
[5,1,+,2,4] => [5,1,3,2,4] => ([(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,9),(1,10),(2,8),(2,10),(3,7),(4,6),(5,1),(5,2),(5,6),(6,8),(6,9),(8,11),(9,11),(10,3),(10,11),(11,7)],12)
=> ? = 4 + 2
[5,1,-,2,4] => [5,1,3,2,4] => ([(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,4),(0,5),(1,9),(1,10),(2,8),(2,10),(3,7),(4,6),(5,1),(5,2),(5,6),(6,8),(6,9),(8,11),(9,11),(10,3),(10,11),(11,7)],12)
=> ? = 4 + 2
[+,+,+,+,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[-,+,+,+,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[+,-,+,+,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[+,+,-,+,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[+,+,+,-,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[-,-,+,+,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[-,+,-,+,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[-,+,+,-,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[+,-,-,+,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[+,-,+,-,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[+,+,-,-,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[-,-,-,+,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[-,-,+,-,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[-,+,-,-,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[+,-,-,-,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[-,-,-,-,6,5] => [1,2,3,4,6,5] => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([(0,5),(1,7),(2,7),(3,4),(4,6),(5,3),(6,1),(6,2)],8)
=> ? = 5 + 2
[+,+,+,6,4,5] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)
=> ? = 5 + 2
[-,+,+,6,4,5] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)
=> ? = 5 + 2
[+,-,+,6,4,5] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)
=> ? = 5 + 2
[+,+,-,6,4,5] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)
=> ? = 5 + 2
[-,-,+,6,4,5] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)
=> ? = 5 + 2
[-,+,-,6,4,5] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)
=> ? = 5 + 2
[+,-,-,6,4,5] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)
=> ? = 5 + 2
[-,-,-,6,4,5] => [1,2,3,6,4,5] => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ([(0,5),(1,8),(2,7),(3,6),(4,1),(4,7),(5,3),(6,2),(6,4),(7,8)],9)
=> ? = 5 + 2
[+,+,4,3,+,+] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 5 + 2
[-,+,4,3,+,+] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 5 + 2
[+,-,4,3,+,+] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 5 + 2
[+,+,4,3,-,+] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 5 + 2
[+,+,4,3,+,-] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 5 + 2
[-,-,4,3,+,+] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 5 + 2
[-,+,4,3,-,+] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 5 + 2
[-,+,4,3,+,-] => [1,2,4,3,5,6] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> ([(0,5),(2,7),(3,7),(4,1),(5,6),(6,2),(6,3),(7,4)],8)
=> ? = 5 + 2
Description
The number of simple modules with projective dimension at most 1.
Matching statistic: St000080
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000080: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000080: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Values
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[+,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[+,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[+,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[+,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 3
[+,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[-,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[+,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[-,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[+,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[-,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 3
[4,1,2,3] => [4,1,2,3] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 3
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,-,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[-,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[+,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4
[-,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4
[+,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4
[+,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4
[-,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4
[-,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4
[+,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4
[-,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4
[+,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
[-,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
[+,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
[-,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4
[+,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4
[-,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4
[+,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4
[+,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4
[-,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4
[-,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4
[+,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4
[-,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4
[+,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4
[-,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4
[+,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4
[-,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4
[+,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4
[-,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4
[+,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4
[-,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4
[5,1,+,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4
[5,1,-,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4
[+,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[-,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[+,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[+,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[+,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[-,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[-,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[-,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[+,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[+,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[+,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[-,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[-,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[-,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[+,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[-,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5
[+,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5
[-,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5
Description
The rank of the poset.
Matching statistic: St000528
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000528: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000528: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Values
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[-,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[+,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[-,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[+,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[-,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[4,1,2,3] => [4,1,2,3] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[-,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[+,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[-,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[+,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 + 1
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 + 1
[+,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 + 1
[-,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 + 1
[+,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[-,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[+,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[-,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[5,1,+,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[5,1,-,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5 + 1
[-,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5 + 1
Description
The height of a poset.
This equals the rank of the poset [[St000080]] plus one.
Matching statistic: St000906
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000906: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000906: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Values
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[-,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[+,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[-,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[+,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[-,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[4,1,2,3] => [4,1,2,3] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[-,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[+,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[-,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[+,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 + 1
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 + 1
[+,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 + 1
[-,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 + 1
[+,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[-,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[+,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[-,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[5,1,+,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[5,1,-,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5 + 1
[-,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5 + 1
Description
The length of the shortest maximal chain in a poset.
Matching statistic: St001636
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001636: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001636: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Values
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[-,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[+,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[-,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[+,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[-,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 4 = 3 + 1
[4,1,2,3] => [4,1,2,3] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 4 = 3 + 1
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,-,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[-,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 4 + 1
[+,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[-,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[+,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[-,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 1
[+,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[-,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 + 1
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 + 1
[+,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 + 1
[-,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 + 1
[+,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[-,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 1
[+,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[-,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[+,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[-,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 1
[5,1,+,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[5,1,-,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 1
[+,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[-,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 1
[+,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5 + 1
[-,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5 + 1
Description
The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset.
Matching statistic: St000642
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000642: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000642: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Values
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[-,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[+,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[-,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[+,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[-,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[4,1,2,3] => [4,1,2,3] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[-,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[+,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[+,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[-,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[-,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[+,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[-,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[+,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 2
[-,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 2
[+,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 2
[-,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 2
[+,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[-,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[+,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[+,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[-,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[-,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[+,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[-,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 + 2
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 + 2
[+,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 + 2
[-,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 + 2
[+,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[-,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[+,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 2
[-,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 2
[+,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 2
[-,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 2
[5,1,+,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[5,1,-,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[+,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5 + 2
[-,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5 + 2
Description
The size of the smallest orbit of antichains under Panyushev complementation.
Matching statistic: St000643
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000643: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000643: Posets ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 75%
Values
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,+,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,-,+,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,+,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,+,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,-,-,+] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,-,+,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,+,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[-,+,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[+,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[-,-,4,3] => [1,2,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[+,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[-,4,2,3] => [1,4,2,3] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 5 = 3 + 2
[4,1,2,3] => [4,1,2,3] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
=> 5 = 3 + 2
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,-,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,-,-,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,-,+,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,-,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,-,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,-,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[-,-,-,-,+] => [1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 6 = 4 + 2
[+,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[-,+,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[+,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[+,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[-,-,+,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[-,+,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[+,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[-,-,-,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[+,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 2
[-,+,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 2
[+,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 2
[-,-,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 4 + 2
[+,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[-,3,2,+,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[+,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[+,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[-,3,2,-,+] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[-,3,2,+,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[+,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[-,3,2,-,-] => [1,3,2,4,5] => [1,3,2,4,5] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[+,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 + 2
[-,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
=> ? = 4 + 2
[+,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 + 2
[-,3,5,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
=> ? = 4 + 2
[+,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[-,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 4 + 2
[+,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 2
[-,5,+,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 2
[+,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 2
[-,5,-,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
=> ? = 4 + 2
[5,1,+,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[5,1,-,2,4] => [5,1,3,2,4] => [3,5,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
=> ? = 4 + 2
[+,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,+,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,-,+,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,+,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,+,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,-,-,+,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,-,+,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,+,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[-,-,-,-,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 5 + 2
[+,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5 + 2
[-,+,+,6,4,5] => [1,2,3,6,4,5] => [1,2,3,6,5,4] => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 5 + 2
Description
The size of the largest orbit of antichains under Panyushev complementation.
The following 114 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001782The order of rowmotion on the set of order ideals of a poset. St001925The minimal number of zeros in a row of an alternating sign matrix. St000890The number of nonzero entries in an alternating sign matrix. St000197The number of entries equal to positive one in the alternating sign matrix. St001556The number of inversions of the third entry of a permutation. St000327The number of cover relations in a poset. St001430The number of positive entries in a signed permutation. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001927Sparre Andersen's number of positives of a signed permutation. St000209Maximum difference of elements in cycles. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. St000809The reduced reflection length of the permutation. St000957The number of Bruhat lower covers of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001429The number of negative entries in a signed permutation. St001480The number of simple summands of the module J^2/J^3. St001557The number of inversions of the second entry of a permutation. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St001958The degree of the polynomial interpolating the values of a permutation. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000501The size of the first part in the decomposition of a permutation. St000673The number of non-fixed points of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001520The number of strict 3-descents. St001948The number of augmented double ascents of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001468The smallest fixpoint of a permutation. St001817The number of flag weak exceedances of a signed permutation. St001892The flag excedance statistic of a signed permutation. St001896The number of right descents of a signed permutations. St001864The number of excedances of a signed permutation. St001866The nesting alignments of a signed permutation. St001964The interval resolution global dimension of a poset. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St000264The girth of a graph, which is not a tree. St000135The number of lucky cars of the parking function. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001768The number of reduced words of a signed permutation. St000188The area of the Dyck path corresponding to a parking function and the total displacement of a parking function. St000195The number of secondary dinversion pairs of the dyck path corresponding to a parking function. St000540The sum of the entries of a parking function minus its length. St000943The number of spots the most unlucky car had to go further in a parking function. St000165The sum of the entries of a parking function. St001209The pmaj statistic of a parking function. St001434The number of negative sum pairs of a signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001926Sparre Andersen's position of the maximum of a signed permutation. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000298The order dimension or Dushnik-Miller dimension of a poset. St000640The rank of the largest boolean interval in a poset. St000744The length of the path to the largest entry in a standard Young tableau. St000907The number of maximal antichains of minimal length in a poset. St001616The number of neutral elements in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001822The number of alignments of a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001870The number of positive entries followed by a negative entry in a signed permutation. St001893The flag descent of a signed permutation. St001935The number of ascents in a parking function. St001937The size of the center of a parking function. St001946The number of descents in a parking function. St000044The number of vertices of the unicellular map given by a perfect matching. St000908The length of the shortest maximal antichain in a poset. St000914The sum of the values of the Möbius function of a poset. St001171The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001613The binary logarithm of the size of the center of a lattice. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001889The size of the connectivity set of a signed permutation. St001895The oddness of a signed permutation. St000017The number of inversions of a standard tableau. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St001301The first Betti number of the order complex associated with the poset. St001371The length of the longest Yamanouchi prefix of a binary word. St001730The number of times the path corresponding to a binary word crosses the base line. St001771The number of occurrences of the signed pattern 1-2 in a signed permutation. St001845The number of join irreducibles minus the rank of a lattice. St001846The number of elements which do not have a complement in the lattice. St001851The number of Hecke atoms of a signed permutation. St001857The number of edges in the reduced word graph of a signed permutation. St001867The number of alignments of type EN of a signed permutation. St001868The number of alignments of type NE of a signed permutation. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001721The degree of a binary word. St001854The size of the left Kazhdan-Lusztig cell, St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St000016The number of attacking pairs of a standard tableau. St000958The number of Bruhat factorizations of a permutation. St001853The size of the two-sided Kazhdan-Lusztig cell, St000417The size of the automorphism group of the ordered tree. St000522The number of 1-protected nodes of a rooted tree. St000679The pruning number of an ordered tree. St001058The breadth of the ordered tree. St000521The number of distinct subtrees of an ordered tree. St000413The number of ordered trees with the same underlying unordered tree. St000415The size of the automorphism group of the rooted tree underlying the ordered tree. St000400The path length of an ordered tree. St000416The number of inequivalent increasing trees of an ordered tree. St000410The tree factorial of an ordered tree.
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