searching the database
Your data matches 19 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000473
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St000473: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000473: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
=> [1]
=> 0
([],2)
=> [2]
=> 1
([(0,1)],2)
=> [1]
=> 0
([],3)
=> [3,3]
=> 2
([(1,2)],3)
=> [3]
=> 1
([(0,1),(0,2)],3)
=> [2]
=> 1
([(0,2),(2,1)],3)
=> [1]
=> 0
([(0,2),(1,2)],3)
=> [2]
=> 1
([(2,3)],4)
=> [4,4,4]
=> 3
([(1,2),(1,3)],4)
=> [8]
=> 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> 2
([(0,2),(0,3),(3,1)],4)
=> [3]
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> 1
([(1,2),(2,3)],4)
=> [4]
=> 1
([(0,3),(3,1),(3,2)],4)
=> [2]
=> 1
([(1,3),(2,3)],4)
=> [8]
=> 1
([(0,3),(1,3),(3,2)],4)
=> [2]
=> 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> 2
([(0,3),(1,2)],4)
=> [4,2]
=> 2
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> 2
([(0,3),(2,1),(3,2)],4)
=> [1]
=> 0
([(0,3),(1,2),(2,3)],4)
=> [3]
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> 2
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> 2
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> 2
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> 2
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> 2
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> 2
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> 1
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> 3
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> 2
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> 3
([(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]
=> 1
Description
The number of parts of a partition that are strictly bigger than the number of ones.
This is part of the definition of Dyson's crank of a partition, see [[St000474]].
Matching statistic: St001280
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St001280: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St001280: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
=> [1]
=> 0
([],2)
=> [2]
=> 1
([(0,1)],2)
=> [1]
=> 0
([],3)
=> [3,3]
=> 2
([(1,2)],3)
=> [3]
=> 1
([(0,1),(0,2)],3)
=> [2]
=> 1
([(0,2),(2,1)],3)
=> [1]
=> 0
([(0,2),(1,2)],3)
=> [2]
=> 1
([(2,3)],4)
=> [4,4,4]
=> 3
([(1,2),(1,3)],4)
=> [8]
=> 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> 2
([(0,2),(0,3),(3,1)],4)
=> [3]
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> 1
([(1,2),(2,3)],4)
=> [4]
=> 1
([(0,3),(3,1),(3,2)],4)
=> [2]
=> 1
([(1,3),(2,3)],4)
=> [8]
=> 1
([(0,3),(1,3),(3,2)],4)
=> [2]
=> 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> 2
([(0,3),(1,2)],4)
=> [4,2]
=> 2
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> 2
([(0,3),(2,1),(3,2)],4)
=> [1]
=> 0
([(0,3),(1,2),(2,3)],4)
=> [3]
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> 2
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> 2
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> 2
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> 2
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> 2
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> 2
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> 1
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> 3
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> 2
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> 3
([(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]
=> 1
Description
The number of parts of an integer partition that are at least two.
Matching statistic: St000147
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000147: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000147: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
=> [1]
=> [1]
=> []
=> 0
([],2)
=> [2]
=> [1,1]
=> [1]
=> 1
([(0,1)],2)
=> [1]
=> [1]
=> []
=> 0
([],3)
=> [3,3]
=> [2,2,2]
=> [2,2]
=> 2
([(1,2)],3)
=> [3]
=> [1,1,1]
=> [1,1]
=> 1
([(0,1),(0,2)],3)
=> [2]
=> [1,1]
=> [1]
=> 1
([(0,2),(2,1)],3)
=> [1]
=> [1]
=> []
=> 0
([(0,2),(1,2)],3)
=> [2]
=> [1,1]
=> [1]
=> 1
([(2,3)],4)
=> [4,4,4]
=> [3,3,3,3]
=> [3,3,3]
=> 3
([(1,2),(1,3)],4)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1]
=> 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [2,2,2]
=> [2,2]
=> 2
([(0,2),(0,3),(3,1)],4)
=> [3]
=> [1,1,1]
=> [1,1]
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> [1,1]
=> [1]
=> 1
([(1,2),(2,3)],4)
=> [4]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(0,3),(3,1),(3,2)],4)
=> [2]
=> [1,1]
=> [1]
=> 1
([(1,3),(2,3)],4)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1]
=> 1
([(0,3),(1,3),(3,2)],4)
=> [2]
=> [1,1]
=> [1]
=> 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [2,2,2]
=> [2,2]
=> 2
([(0,3),(1,2)],4)
=> [4,2]
=> [2,2,1,1]
=> [2,1,1]
=> 2
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [2,2,1]
=> [2,1]
=> 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2,2]
=> [2]
=> 2
([(0,3),(2,1),(3,2)],4)
=> [1]
=> [1]
=> []
=> 0
([(0,3),(1,2),(2,3)],4)
=> [3]
=> [1,1,1]
=> [1,1]
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [3,3,3,3]
=> [3,3,3]
=> 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1]
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [2,2,2]
=> [2,2]
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1]
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [2,2,2,2,2]
=> [2,2,2,2]
=> 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> [1,1]
=> [1]
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [2,2,1,1]
=> [2,1,1]
=> 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [2,2,1]
=> [2,1]
=> 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2,2]
=> [2]
=> 2
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [2,2,2,2,2]
=> [2,2,2,2]
=> 2
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [2,2,2]
=> [2,2]
=> 2
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [2,2,2,2,2]
=> [2,2,2,2]
=> 2
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2,2]
=> [2]
=> 2
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [2,2,2]
=> [2,2]
=> 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [2,2,2,2,2,2]
=> [2,2,2,2,2]
=> 2
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> [1,1]
=> [1]
=> 1
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [3,3,3,3]
=> [3,3,3]
=> 3
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [2,2,2,2,1]
=> [2,2,2,1]
=> 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [2,2,1]
=> [2,1]
=> 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,1,1,1,1,1]
=> [1,1,1,1,1]
=> 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2,2]
=> [2]
=> 2
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> [1,1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> [1,1,1,1]
=> [1,1,1]
=> 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [3,3,3,2]
=> [3,3,2]
=> 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> [1,1,1]
=> [1,1]
=> 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1]
=> 1
Description
The largest part of an integer partition.
Matching statistic: St000143
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000143: Integer partitions ⟶ ℤResult quality: 79% ●values known / values provided: 79%●distinct values known / distinct values provided: 100%
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000143: Integer partitions ⟶ ℤResult quality: 79% ●values known / values provided: 79%●distinct values known / distinct values provided: 100%
Values
([],1)
=> [1]
=> [1]
=> 0
([],2)
=> [2]
=> [1,1]
=> 1
([(0,1)],2)
=> [1]
=> [1]
=> 0
([],3)
=> [3,3]
=> [2,2,2]
=> 2
([(1,2)],3)
=> [3]
=> [1,1,1]
=> 1
([(0,1),(0,2)],3)
=> [2]
=> [1,1]
=> 1
([(0,2),(2,1)],3)
=> [1]
=> [1]
=> 0
([(0,2),(1,2)],3)
=> [2]
=> [1,1]
=> 1
([(2,3)],4)
=> [4,4,4]
=> [3,3,3,3]
=> ? = 3
([(1,2),(1,3)],4)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [2,2,2]
=> 2
([(0,2),(0,3),(3,1)],4)
=> [3]
=> [1,1,1]
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> [1,1]
=> 1
([(1,2),(2,3)],4)
=> [4]
=> [1,1,1,1]
=> 1
([(0,3),(3,1),(3,2)],4)
=> [2]
=> [1,1]
=> 1
([(1,3),(2,3)],4)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 1
([(0,3),(1,3),(3,2)],4)
=> [2]
=> [1,1]
=> 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [2,2,2]
=> 2
([(0,3),(1,2)],4)
=> [4,2]
=> [2,2,1,1]
=> 2
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [2,2,1]
=> 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2,2]
=> 2
([(0,3),(2,1),(3,2)],4)
=> [1]
=> [1]
=> 0
([(0,3),(1,2),(2,3)],4)
=> [3]
=> [1,1,1]
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [3,3,3,3]
=> ? = 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [2,2,2]
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [2,2,2,2,2]
=> 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> [1,1]
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [2,2,1,1]
=> 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [2,2,1]
=> 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2,2]
=> 2
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [2,2,2,2,2]
=> 2
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [2,2,2]
=> 2
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [2,2,2,2,2]
=> 2
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2,2]
=> 2
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [2,2,2]
=> 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> [1,1]
=> 1
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [3,3,3,3]
=> ? = 3
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [2,2,2,2,1]
=> 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [2,2,1]
=> 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2,2]
=> 2
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> [1,1,1,1,1,1,1]
=> 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> [1,1,1,1]
=> 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [3,3,3,2]
=> 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> [1,1,1]
=> 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [2,2,2,1,1]
=> 2
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [2,2,2,2,1]
=> 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,1,1,1,1,1]
=> 1
([(1,4),(3,2),(4,3)],5)
=> [5]
=> [1,1,1,1,1]
=> 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(1,4),(4,5),(5,2),(5,3)],6)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(1,5),(2,5),(3,4),(5,3)],6)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> [4,4,4]
=> [3,3,3,3]
=> ? = 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [2,2,1,1,1,1,1,1,1,1]
=> ? = 2
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
=> [4,4,4]
=> [3,3,3,3]
=> ? = 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
=> [8,3]
=> [2,2,2,1,1,1,1,1]
=> ? = 2
([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
=> [9,3]
=> [2,2,2,1,1,1,1,1,1]
=> ? = 2
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
=> [8,3]
=> [2,2,2,1,1,1,1,1]
=> ? = 2
([(0,5),(4,3),(5,1),(5,2),(5,4)],6)
=> [4,4,4]
=> [3,3,3,3]
=> ? = 3
([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,5),(1,4),(3,2),(4,3),(4,5)],6)
=> [9,3]
=> [2,2,2,1,1,1,1,1,1]
=> ? = 2
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)
=> [4,4,4]
=> [3,3,3,3]
=> ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)
=> [4,4,4]
=> [3,3,3,3]
=> ? = 3
([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7)
=> [10,2]
=> [2,2,1,1,1,1,1,1,1,1]
=> ? = 2
([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7)
=> [8,3]
=> [2,2,2,1,1,1,1,1]
=> ? = 2
([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7)
=> [9,3]
=> [2,2,2,1,1,1,1,1,1]
=> ? = 2
([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7)
=> [9,3]
=> [2,2,2,1,1,1,1,1,1]
=> ? = 2
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7)
=> [8,3]
=> [2,2,2,1,1,1,1,1]
=> ? = 2
([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)
=> [6,6]
=> [2,2,2,2,2,2]
=> ? = 2
([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> ? = 1
Description
The largest repeated part of a partition.
If the parts of the partition are all distinct, the value of the statistic is defined to be zero.
Matching statistic: St000678
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St000678: Dyck paths ⟶ ℤResult quality: 78% ●values known / values provided: 78%●distinct values known / distinct values provided: 80%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St000678: Dyck paths ⟶ ℤResult quality: 78% ●values known / values provided: 78%●distinct values known / distinct values provided: 80%
Values
([],1)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([],2)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,1)],2)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([],3)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(1,2)],3)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,1),(0,2)],3)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,2),(2,1)],3)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,2),(1,2)],3)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(2,3)],4)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 3
([(1,2),(1,3)],4)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,2),(0,3),(3,1)],4)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(1,2),(2,3)],4)
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 1
([(0,3),(3,1),(3,2)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(1,3),(2,3)],4)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,3),(1,3),(3,2)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,3),(1,2)],4)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(0,3),(2,1),(3,2)],4)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,3),(1,2),(2,3)],4)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 2
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 3
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 1
([(1,4),(3,2),(4,3)],5)
=> [5]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
([(0,3),(3,4),(4,1),(4,2)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,4),(3,2),(4,1),(4,3)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> [7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,4),(4,5),(5,2),(5,3)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,5),(2,5),(3,4),(5,3)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,4),(3,2),(4,3),(4,5)],6)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)
=> [10]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 2
([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
Description
The number of up steps after the last double rise of a Dyck path.
Matching statistic: St001039
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001039: Dyck paths ⟶ ℤResult quality: 78% ●values known / values provided: 78%●distinct values known / distinct values provided: 80%
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001039: Dyck paths ⟶ ℤResult quality: 78% ●values known / values provided: 78%●distinct values known / distinct values provided: 80%
Values
([],1)
=> [1]
=> [1]
=> [1,0]
=> ? = 0
([],2)
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 1
([(0,1)],2)
=> [1]
=> [1]
=> [1,0]
=> ? = 0
([],3)
=> [3,3]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> 2
([(1,2)],3)
=> [3]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 1
([(0,1),(0,2)],3)
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 1
([(0,2),(2,1)],3)
=> [1]
=> [1]
=> [1,0]
=> ? = 0
([(0,2),(1,2)],3)
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 1
([(2,3)],4)
=> [4,4,4]
=> [3,3,3,3]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 3
([(1,2),(1,3)],4)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> 2
([(0,2),(0,3),(3,1)],4)
=> [3]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 1
([(1,2),(2,3)],4)
=> [4]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 1
([(0,3),(3,1),(3,2)],4)
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 1
([(1,3),(2,3)],4)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,3),(1,3),(3,2)],4)
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> 2
([(0,3),(1,2)],4)
=> [4,2]
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> 2
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> 2
([(0,3),(2,1),(3,2)],4)
=> [1]
=> [1]
=> [1,0]
=> ? = 0
([(0,3),(1,2),(2,3)],4)
=> [3]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [3,3,3,3]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [2,2,2,2,2]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> 2
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [2,2,2,2,2]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 2
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> 2
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [2,2,2,2,2]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 2
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> 2
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [2,2,2,2,2,2]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> 2
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 1
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [3,3,3,3]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 3
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [2,2,2,2,1]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2,2]
=> [1,1,1,0,0,0]
=> 2
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [3,3,3,2]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [2,2,2,2,2,2]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [2,2,2,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> 2
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [2,2,2,2,1]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 1
([(1,4),(3,2),(4,3)],5)
=> [5]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1
([(0,3),(3,4),(4,1),(4,2)],5)
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> [3]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [2,2,2,2,2]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 2
([(0,4),(3,2),(4,1),(4,3)],5)
=> [3]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> [7]
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> [1]
=> [1]
=> [1,0]
=> ? = 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,4),(4,5),(5,2),(5,3)],6)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(1,5),(2,5),(3,4),(5,3)],6)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> ? = 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [2,2,1,1,1,1,1,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> [6,2,2]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> ? = 3
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
=> [8,3]
=> [2,2,2,1,1,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
=> [9,3]
=> [2,2,2,1,1,1,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
=> [8,3]
=> [2,2,2,1,1,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,5),(1,4),(3,2),(4,3),(4,5)],6)
=> [9,3]
=> [2,2,2,1,1,1,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> [1]
=> [1]
=> [1,0]
=> ? = 0
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
=> [6,2,2]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> ? = 3
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)
=> [6,2,2]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> ? = 3
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)
=> [6,2,2]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)
=> [6,2,2]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> ? = 3
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)
=> [10]
=> [1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)
=> [6,2,2]
=> [3,3,1,1,1,1]
=> [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]
=> ? = 3
([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7)
=> [10,2]
=> [2,2,1,1,1,1,1,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7)
=> [8,3]
=> [2,2,2,1,1,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7)
=> [9,3]
=> [2,2,2,1,1,1,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> [8]
=> [1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7)
=> [9,3]
=> [2,2,2,1,1,1,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7)
=> [8,3]
=> [2,2,2,1,1,1,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 2
([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
=> [12]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 1
Description
The maximal height of a column in the parallelogram polyomino associated with a Dyck path.
Matching statistic: St001418
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001418: Dyck paths ⟶ ℤResult quality: 78% ●values known / values provided: 78%●distinct values known / distinct values provided: 80%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001418: Dyck paths ⟶ ℤResult quality: 78% ●values known / values provided: 78%●distinct values known / distinct values provided: 80%
Values
([],1)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([],2)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,1)],2)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([],3)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(1,2)],3)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,1),(0,2)],3)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,2),(2,1)],3)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,2),(1,2)],3)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(2,3)],4)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 3
([(1,2),(1,3)],4)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,2),(0,3),(3,1)],4)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(1,2),(2,3)],4)
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 1
([(0,3),(3,1),(3,2)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(1,3),(2,3)],4)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,3),(1,3),(3,2)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,3),(1,2)],4)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(0,3),(2,1),(3,2)],4)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,3),(1,2),(2,3)],4)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 2
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 3
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 1
([(1,4),(3,2),(4,3)],5)
=> [5]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
([(0,3),(3,4),(4,1),(4,2)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,4),(3,2),(4,1),(4,3)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> [7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,4),(4,5),(5,2),(5,3)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,5),(2,5),(3,4),(5,3)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,4),(3,2),(4,3),(4,5)],6)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)
=> [10]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 2
([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
Description
Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path.
The stable Auslander algebra is by definition the stable endomorphism ring of the direct sum of all indecomposable modules.
Matching statistic: St001499
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001499: Dyck paths ⟶ ℤResult quality: 78% ●values known / values provided: 78%●distinct values known / distinct values provided: 80%
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001499: Dyck paths ⟶ ℤResult quality: 78% ●values known / values provided: 78%●distinct values known / distinct values provided: 80%
Values
([],1)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([],2)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,1)],2)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([],3)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(1,2)],3)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,1),(0,2)],3)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,2),(2,1)],3)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,2),(1,2)],3)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(2,3)],4)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 3
([(1,2),(1,3)],4)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,2),(0,3),(3,1)],4)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(1,2),(2,3)],4)
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 1
([(0,3),(3,1),(3,2)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(1,3),(2,3)],4)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,3),(1,3),(3,2)],4)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,3),(1,2)],4)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(0,3),(2,1),(3,2)],4)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,3),(1,2),(2,3)],4)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 2
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 3
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> 2
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 2
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> 1
([(1,4),(3,2),(4,3)],5)
=> [5]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
([(0,3),(3,4),(4,1),(4,2)],5)
=> [2]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 2
([(0,4),(3,2),(4,1),(4,3)],5)
=> [3]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> [7]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,4),(4,5),(5,2),(5,3)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(1,5),(2,5),(3,4),(5,3)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 2
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,4),(1,3),(1,5),(4,5),(5,2)],6)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,4),(3,2),(4,3),(4,5)],6)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> [1]
=> [1,0]
=> [1,0]
=> ? = 0
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)
=> [10]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)
=> [6,2,2]
=> [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]
=> ? = 3
([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7)
=> [10,2]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]
=> ? = 2
([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> [8]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7)
=> [9,3]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7)
=> [8,3]
=> [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]
=> ? = 2
([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
=> [12]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
=> ? = 1
Description
The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra.
We use the bijection in the code by Christian Stump to have a bijection to Dyck paths.
Matching statistic: St000668
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 60%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 60%
Values
([],1)
=> [1]
=> []
=> []
=> ? = 0 - 1
([],2)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(0,1)],2)
=> [1]
=> []
=> []
=> ? = 0 - 1
([],3)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(1,2)],3)
=> [3]
=> []
=> []
=> ? = 1 - 1
([(0,1),(0,2)],3)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(0,2),(2,1)],3)
=> [1]
=> []
=> []
=> ? = 0 - 1
([(0,2),(1,2)],3)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(2,3)],4)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 2 = 3 - 1
([(1,2),(1,3)],4)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(0,2),(0,3),(3,1)],4)
=> [3]
=> []
=> []
=> ? = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(1,2),(2,3)],4)
=> [4]
=> []
=> []
=> ? = 1 - 1
([(0,3),(3,1),(3,2)],4)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(1,3),(2,3)],4)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(0,3),(1,3),(3,2)],4)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(0,3),(1,2)],4)
=> [4,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,3),(2,1),(3,2)],4)
=> [1]
=> []
=> []
=> ? = 0 - 1
([(0,3),(1,2),(2,3)],4)
=> [3]
=> []
=> []
=> ? = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 2 = 3 - 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 2 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 2 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 2 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 2 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 2 = 3 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [4]
=> [1,1,1,1]
=> 1 = 2 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> []
=> []
=> ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> []
=> []
=> ? = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> []
=> []
=> ? = 1 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [4,3]
=> [2,2,2,1]
=> 2 = 3 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> []
=> []
=> ? = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [4]
=> [1,1,1,1]
=> 1 = 2 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> []
=> []
=> ? = 1 - 1
([(1,4),(3,2),(4,3)],5)
=> [5]
=> []
=> []
=> ? = 1 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
=> [3]
=> []
=> []
=> ? = 1 - 1
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 2 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
=> [3]
=> []
=> []
=> ? = 1 - 1
([(0,4),(1,2),(2,3),(2,4)],5)
=> [7]
=> []
=> []
=> ? = 1 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
=> [1]
=> []
=> []
=> ? = 0 - 1
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
=> [4]
=> []
=> []
=> ? = 1 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 2 - 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [12]
=> []
=> []
=> ? = 1 - 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [6]
=> []
=> []
=> ? = 1 - 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
=> [7]
=> []
=> []
=> ? = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 2 - 1
([(1,4),(4,5),(5,2),(5,3)],6)
=> [12]
=> []
=> []
=> ? = 1 - 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 1 = 2 - 1
([(1,5),(2,5),(3,4),(5,3)],6)
=> [12]
=> []
=> []
=> ? = 1 - 1
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [6]
=> []
=> []
=> ? = 1 - 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> [4,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 2 = 3 - 1
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> [2]
=> []
=> []
=> ? = 1 - 1
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 2 - 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 1 = 2 - 1
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 1 = 2 - 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [2,2]
=> [2,2]
=> 2 = 3 - 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> [3,2]
=> [2]
=> [1,1]
=> 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> [6]
=> []
=> []
=> ? = 1 - 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> [3]
=> []
=> []
=> ? = 1 - 1
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [8]
=> []
=> []
=> ? = 1 - 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> [4]
=> []
=> []
=> ? = 1 - 1
Description
The least common multiple of the parts of the partition.
Matching statistic: St001918
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001918: Integer partitions ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 60%
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St001918: Integer partitions ⟶ ℤResult quality: 60% ●values known / values provided: 60%●distinct values known / distinct values provided: 60%
Values
([],1)
=> [1]
=> []
=> []
=> ? = 0 - 2
([],2)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(0,1)],2)
=> [1]
=> []
=> []
=> ? = 0 - 2
([],3)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(1,2)],3)
=> [3]
=> []
=> []
=> ? = 1 - 2
([(0,1),(0,2)],3)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(0,2),(2,1)],3)
=> [1]
=> []
=> []
=> ? = 0 - 2
([(0,2),(1,2)],3)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(2,3)],4)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 3 - 2
([(1,2),(1,3)],4)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(0,1),(0,2),(0,3)],4)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(0,2),(0,3),(3,1)],4)
=> [3]
=> []
=> []
=> ? = 1 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(1,2),(2,3)],4)
=> [4]
=> []
=> []
=> ? = 1 - 2
([(0,3),(3,1),(3,2)],4)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(1,3),(2,3)],4)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(0,3),(1,3),(3,2)],4)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(0,3),(1,3),(2,3)],4)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(0,3),(1,2)],4)
=> [4,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,3),(1,2),(1,3)],4)
=> [3,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,2),(0,3),(1,2),(1,3)],4)
=> [2,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,3),(2,1),(3,2)],4)
=> [1]
=> []
=> []
=> ? = 0 - 2
([(0,3),(1,2),(2,3)],4)
=> [3]
=> []
=> []
=> ? = 1 - 2
([(0,2),(0,3),(0,4),(4,1)],5)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 3 - 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(1,2),(1,3),(2,4),(3,4)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(0,3),(0,4),(3,2),(4,1)],5)
=> [4,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> [3,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(1,4),(4,2),(4,3)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0 = 2 - 2
([(0,4),(4,1),(4,2),(4,3)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(1,4),(2,4),(4,3)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0 = 2 - 2
([(0,4),(1,4),(4,2),(4,3)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,4),(1,4),(2,4),(4,3)],5)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0 = 2 - 2
([(0,4),(1,4),(2,3),(4,2)],5)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(0,4),(1,3),(2,3),(3,4)],5)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(0,4),(1,4),(2,3),(3,4)],5)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 3 - 2
([(0,4),(1,2),(1,4),(2,3)],5)
=> [5,4]
=> [4]
=> [1,1,1,1]
=> 0 = 2 - 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> [3,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> [6]
=> []
=> []
=> ? = 1 - 2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> [2,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,4),(1,2),(1,4),(4,3)],5)
=> [7]
=> []
=> []
=> ? = 1 - 2
([(0,2),(0,4),(3,1),(4,3)],5)
=> [4]
=> []
=> []
=> ? = 1 - 2
([(0,4),(1,2),(1,3),(3,4)],5)
=> [4,4,3]
=> [4,3]
=> [2,2,2,1]
=> 1 = 3 - 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> [3]
=> []
=> []
=> ? = 1 - 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> [5,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(0,3),(1,2),(1,4),(3,4)],5)
=> [5,4]
=> [4]
=> [1,1,1,1]
=> 0 = 2 - 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> [6]
=> []
=> []
=> ? = 1 - 2
([(1,4),(3,2),(4,3)],5)
=> [5]
=> []
=> []
=> ? = 1 - 2
([(0,3),(3,4),(4,1),(4,2)],5)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(0,4),(1,2),(2,4),(4,3)],5)
=> [3]
=> []
=> []
=> ? = 1 - 2
([(0,3),(1,4),(4,2)],5)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0 = 2 - 2
([(0,4),(3,2),(4,1),(4,3)],5)
=> [3]
=> []
=> []
=> ? = 1 - 2
([(0,4),(1,2),(2,3),(2,4)],5)
=> [7]
=> []
=> []
=> ? = 1 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
=> [1]
=> []
=> []
=> ? = 0 - 2
([(0,3),(1,2),(2,4),(3,4)],5)
=> [4,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,4),(1,2),(2,3),(3,4)],5)
=> [4]
=> []
=> []
=> ? = 1 - 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0 = 2 - 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0 = 2 - 2
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [12]
=> []
=> []
=> ? = 1 - 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> [6]
=> []
=> []
=> ? = 1 - 2
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
=> [7]
=> []
=> []
=> ? = 1 - 2
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0 = 2 - 2
([(1,4),(4,5),(5,2),(5,3)],6)
=> [12]
=> []
=> []
=> ? = 1 - 2
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0 = 2 - 2
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0 = 2 - 2
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> [6,6]
=> [6]
=> [1,1,1,1,1,1]
=> 0 = 2 - 2
([(1,5),(2,5),(3,4),(5,3)],6)
=> [12]
=> []
=> []
=> ? = 1 - 2
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> [6]
=> []
=> []
=> ? = 1 - 2
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0 = 2 - 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
=> [4,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
=> [4,4,4]
=> [4,4]
=> [2,2,2,2]
=> 1 = 3 - 2
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> [2]
=> []
=> []
=> ? = 1 - 2
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0 = 2 - 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
=> [3,3]
=> [3]
=> [1,1,1]
=> 0 = 2 - 2
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
=> [5,5]
=> [5]
=> [1,1,1,1,1]
=> 0 = 2 - 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> [2,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> [6,2,2]
=> [2,2]
=> [2,2]
=> 1 = 3 - 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> [3,2]
=> [2]
=> [1,1]
=> 0 = 2 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> [6]
=> []
=> []
=> ? = 1 - 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> [3]
=> []
=> []
=> ? = 1 - 2
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
=> [8]
=> []
=> []
=> ? = 1 - 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
=> [4]
=> []
=> []
=> ? = 1 - 2
Description
The degree of the cyclic sieving polynomial corresponding to an integer partition.
Let λ be an integer partition of n and let N be the least common multiple of the parts of λ. Fix an arbitrary permutation π of cycle type λ. Then π induces a cyclic action of order N on {1,…,n}.
The corresponding character can be identified with the cyclic sieving polynomial Cλ(q) of this action, modulo qN−1. Explicitly, it is
∑p∈λ[p]qN/p,
where [p]q=1+⋯+qp−1 is the q-integer.
This statistic records the degree of Cλ(q). Equivalently, it equals
(1−1λ1)N,
where λ1 is the largest part of λ.
The statistic is undefined for the empty partition.
The following 9 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001200The number of simple modules in eAe with projective dimension at most 2 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. St001333The cardinality of a minimal edge-isolating set of a graph. St001393The induced matching number of a graph. St000482The (zero)-forcing number of a graph. St000778The metric dimension of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001352The number of internal nodes in the modular decomposition of a graph.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!