Identifier
-
Mp00307:
Posets
—promotion cycle type⟶
Integer partitions
St000944: Integer partitions ⟶ ℤ
Values
([],1) => [1] => 0
([],2) => [2] => 0
([(0,1)],2) => [1] => 0
([],3) => [3,3] => 6
([(1,2)],3) => [3] => 1
([(0,1),(0,2)],3) => [2] => 0
([(0,2),(2,1)],3) => [1] => 0
([(0,2),(1,2)],3) => [2] => 0
([(1,2),(1,3)],4) => [8] => 2
([(0,1),(0,2),(0,3)],4) => [3,3] => 6
([(0,2),(0,3),(3,1)],4) => [3] => 1
([(0,1),(0,2),(1,3),(2,3)],4) => [2] => 0
([(1,2),(2,3)],4) => [4] => 1
([(0,3),(3,1),(3,2)],4) => [2] => 0
([(1,3),(2,3)],4) => [8] => 2
([(0,3),(1,3),(3,2)],4) => [2] => 0
([(0,3),(1,3),(2,3)],4) => [3,3] => 6
([(0,3),(1,2)],4) => [4,2] => 0
([(0,3),(1,2),(1,3)],4) => [3,2] => 1
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2] => 1
([(0,3),(2,1),(3,2)],4) => [1] => 0
([(0,3),(1,2),(2,3)],4) => [3] => 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => [8] => 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => [3,3] => 6
([(0,3),(0,4),(4,1),(4,2)],5) => [8] => 2
([(1,2),(1,3),(2,4),(3,4)],5) => [5,5] => 85
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [2] => 0
([(0,3),(0,4),(3,2),(4,1)],5) => [4,2] => 0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => [3,2] => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [2,2] => 1
([(1,4),(4,2),(4,3)],5) => [5,5] => 85
([(0,4),(4,1),(4,2),(4,3)],5) => [3,3] => 6
([(1,4),(2,4),(4,3)],5) => [5,5] => 85
([(0,4),(1,4),(4,2),(4,3)],5) => [2,2] => 1
([(0,4),(1,4),(2,4),(4,3)],5) => [3,3] => 6
([(0,4),(1,4),(2,3),(4,2)],5) => [2] => 0
([(0,4),(1,3),(2,3),(3,4)],5) => [8] => 2
([(0,4),(1,2),(1,4),(2,3)],5) => [5,4] => 85
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => [3,2] => 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => [6] => 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [2,2] => 1
([(0,4),(1,2),(1,4),(4,3)],5) => [7] => 2
([(0,2),(0,4),(3,1),(4,3)],5) => [4] => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [3] => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [8] => 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => [5,3] => 56
([(0,3),(1,2),(1,4),(3,4)],5) => [5,4] => 85
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => [6] => 2
([(1,4),(3,2),(4,3)],5) => [5] => 1
([(0,3),(3,4),(4,1),(4,2)],5) => [2] => 0
([(0,4),(1,2),(2,4),(4,3)],5) => [3] => 1
([(0,3),(1,4),(4,2)],5) => [5,5] => 85
([(0,4),(3,2),(4,1),(4,3)],5) => [3] => 1
([(0,4),(1,2),(2,3),(2,4)],5) => [7] => 2
([(0,4),(2,3),(3,1),(4,2)],5) => [1] => 0
([(0,3),(1,2),(2,4),(3,4)],5) => [4,2] => 0
([(0,4),(1,2),(2,3),(3,4)],5) => [4] => 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [2] => 0
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6) => [3,3] => 6
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6) => [8] => 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6) => [5,5] => 85
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [2,2] => 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => [6] => 2
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [2,2] => 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) => [7] => 2
([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => [3,3] => 6
([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => [3,3] => 6
([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => [8] => 2
([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => [6] => 2
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [2,2] => 1
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6) => [5,5] => 85
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => [4,2] => 0
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6) => [8] => 2
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [2] => 0
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [8] => 2
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [5,5] => 85
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6) => [3,3] => 6
([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => [5,5] => 85
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [2,2] => 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => [6,2,2] => 351
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => [3,2] => 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => [6,2,2] => 351
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => [2,2,2,2] => 13
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) => [4,4] => 15
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => [2,2] => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => [6] => 2
([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => [5,5] => 85
([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => [5,5] => 85
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) => [5,4] => 85
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => [3,2] => 1
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) => [5,4] => 85
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => [5,3] => 56
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [3] => 1
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [8] => 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => [4] => 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [2] => 0
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6) => [5,5] => 85
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => [5,3] => 56
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => [6] => 2
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) => [7] => 2
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => [3,3,3] => 63
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Description
The 3-degree of an integer partition.
For an integer partition $\lambda$, this is given by the exponent of 3 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$.
This stupid comment should not be accepted as an edit!
For an integer partition $\lambda$, this is given by the exponent of 3 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$.
This stupid comment should not be accepted as an edit!
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.
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