Loading [MathJax]/jax/output/HTML-CSS/jax.js

Your data matches 6 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001420
(load all 4 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001420: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1]
 => 10 => 1
([],2)
 => [2]
 => 100 => 1
([(0,1)],2)
 => [1]
 => 10 => 1
([],3)
 => [3,3]
 => 11000 => 2
([(1,2)],3)
 => [3]
 => 1000 => 1
([(0,1),(0,2)],3)
 => [2]
 => 100 => 1
([(0,2),(2,1)],3)
 => [1]
 => 10 => 1
([(0,2),(1,2)],3)
 => [2]
 => 100 => 1
([(2,3)],4)
 => [4,4,4]
 => 1110000 => 3
([(1,2),(1,3)],4)
 => [8]
 => 100000000 => 1
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => 11000 => 2
([(0,2),(0,3),(3,1)],4)
 => [3]
 => 1000 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => 100 => 1
([(1,2),(2,3)],4)
 => [4]
 => 10000 => 1
([(0,3),(3,1),(3,2)],4)
 => [2]
 => 100 => 1
([(1,3),(2,3)],4)
 => [8]
 => 100000000 => 1
([(0,3),(1,3),(3,2)],4)
 => [2]
 => 100 => 1
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => 11000 => 2
([(0,3),(1,2)],4)
 => [4,2]
 => 100100 => 1
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => 10100 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => 1100 => 2
([(0,3),(2,1),(3,2)],4)
 => [1]
 => 10 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => 1000 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => 1110000 => 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => 100000000 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => 11000 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => 100000000 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => 1100000 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => 100 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => 100100 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => 10100 => 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => 1100 => 2
([(2,3),(3,4)],5)
 => [5,5,5,5]
 => 111100000 => 4
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => 1100000 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => 11000 => 2
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => 1100000 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => 1100 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => 11000 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => 11000000 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => 100 => 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => 100000000 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => 1110000 => 3
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => 1010000 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => 10100 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => 111100000 => 4
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => 1000000 => 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => 1100 => 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => 10000000 => 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => 10000 => 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => 1101000 => 3
Description
Half the length of a longest factor which is its own reverse-complement of a binary word.
Matching statistic: St001421
(load all 2 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001421: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => [1]
 => 10 => 1
([],2)
 => [2]
 => 100 => 1
([(0,1)],2)
 => [1]
 => 10 => 1
([],3)
 => [3,3]
 => 11000 => 2
([(1,2)],3)
 => [3]
 => 1000 => 1
([(0,1),(0,2)],3)
 => [2]
 => 100 => 1
([(0,2),(2,1)],3)
 => [1]
 => 10 => 1
([(0,2),(1,2)],3)
 => [2]
 => 100 => 1
([(2,3)],4)
 => [4,4,4]
 => 1110000 => 3
([(1,2),(1,3)],4)
 => [8]
 => 100000000 => 1
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => 11000 => 2
([(0,2),(0,3),(3,1)],4)
 => [3]
 => 1000 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => 100 => 1
([(1,2),(2,3)],4)
 => [4]
 => 10000 => 1
([(0,3),(3,1),(3,2)],4)
 => [2]
 => 100 => 1
([(1,3),(2,3)],4)
 => [8]
 => 100000000 => 1
([(0,3),(1,3),(3,2)],4)
 => [2]
 => 100 => 1
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => 11000 => 2
([(0,3),(1,2)],4)
 => [4,2]
 => 100100 => 1
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => 10100 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => 1100 => 2
([(0,3),(2,1),(3,2)],4)
 => [1]
 => 10 => 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => 1000 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => 1110000 => 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => 100000000 => 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => 11000 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => 100000000 => 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => 1100000 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => 100 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => 100100 => 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => 10100 => 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => 1100 => 2
([(2,3),(3,4)],5)
 => [5,5,5,5]
 => 111100000 => 4
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => 1100000 => 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => 11000 => 2
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => 1100000 => 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => 1100 => 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => 11000 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => 11000000 => 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => 100 => 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => 100000000 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => 1110000 => 3
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => 1010000 => 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => 10100 => 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => 111100000 => 4
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => 1000000 => 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => 1100 => 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => 10000000 => 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => 10000 => 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => 1101000 => 3
Description
Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word.
Matching statistic: St001526
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001526: Dyck paths ⟶ ℤResult quality: 33% ●values known / values provided: 33%●distinct values known / distinct values provided: 50%
Values
([],1)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2 = 1 + 1
([],2)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,1)],2)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2 = 1 + 1
([],3)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(1,2)],3)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => 2 = 1 + 1
([(0,1),(0,2)],3)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,2),(2,1)],3)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2 = 1 + 1
([(0,2),(1,2)],3)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(2,3)],4)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
([(1,2),(1,3)],4)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,2),(0,3),(3,1)],4)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => 2 = 1 + 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(1,2),(2,3)],4)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 2 = 1 + 1
([(0,3),(3,1),(3,2)],4)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(1,3),(2,3)],4)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,3),(1,3),(3,2)],4)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,3),(1,2)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 3 = 2 + 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 3 = 2 + 1
([(0,3),(2,1),(3,2)],4)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2 = 1 + 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 3 = 2 + 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 3 = 2 + 1
([(2,3),(3,4)],5)
 => [5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 4 + 1
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 3 = 2 + 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 3 = 2 + 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 4 + 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 3 = 2 + 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 2 = 1 + 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => [4,4,3]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0]
 => ? = 3 + 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => 2 = 1 + 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => [5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => 2 = 1 + 1
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => 2 = 1 + 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => [1,0,1,0]
 => [1,1,0,0]
 => 2 = 1 + 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 2 = 1 + 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 4 + 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 3 = 2 + 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 3 = 2 + 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
 => [3,3,3,3,3,3]
 => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 3 = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
 => [4,4,4]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [2]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 2 = 1 + 1
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => [5,5,5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 4 + 1
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => [5,5]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => [6,2,2]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,1,0,0,1,0]
 => ? = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
 => [4,4,2,2]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => ? = 4 + 1
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => [6,2,2]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,1,0,0,1,0]
 => ? = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
 => [2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 2 + 1
Description
The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001232
(load all 3 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 25% ●values known / values provided: 29%●distinct values known / distinct values provided: 25%
Values
([],1)
 => [1]
 => [1,0]
 => [1,0]
 => 0 = 1 - 1
([],2)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(0,1)],2)
 => [1]
 => [1,0]
 => [1,0]
 => 0 = 1 - 1
([],3)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2 - 1
([(1,2)],3)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 1 - 1
([(0,1),(0,2)],3)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(0,2),(2,1)],3)
 => [1]
 => [1,0]
 => [1,0]
 => 0 = 1 - 1
([(0,2),(1,2)],3)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(2,3)],4)
 => [4,4,4]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 3 - 1
([(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 - 1
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,2),(0,3),(3,1)],4)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(1,2),(2,3)],4)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 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 - 1
([(0,3),(1,3),(3,2)],4)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,3),(1,2)],4)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => ? = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => [1]
 => [1,0]
 => [1,0]
 => 0 = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 1 - 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]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 3 - 1
([(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 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2 - 1
([(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
([(1,2),(1,3),(2,4),(3,4)],5)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => ? = 1 - 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 2 - 1
([(2,3),(3,4)],5)
 => [5,5,5,5]
 => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 4 - 1
([(1,4),(4,2),(4,3)],5)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2 - 1
([(1,4),(2,4),(4,3)],5)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 2 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2 - 1
([(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]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 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 - 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]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 3 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 4 - 1
([(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]
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 2 - 1
([(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]
 => 0 = 1 - 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]
 => 0 = 1 - 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]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 1 - 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 - 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]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(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]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => ? = 1 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => [5,4]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(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]
 => 0 = 1 - 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]
 => 0 = 1 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 1 - 1
([(0,3),(1,4),(4,2)],5)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 1 - 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]
 => 0 = 1 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => [1,0]
 => [1,0]
 => 0 = 1 - 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 1 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [6,6]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(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
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
 => [5,5,5,5]
 => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 4 - 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [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]
 => 0 = 1 - 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 2 - 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [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]
 => 0 = 1 - 1
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [6,6]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
 => [6,6]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)
 => [6,6]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)
 => [3,3,3,3,3,3]
 => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 3 - 1
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
 => [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]
 => 0 = 1 - 1
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
 => [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]
 => 0 = 1 - 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 1 - 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 1 - 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
 => [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]
 => 0 = 1 - 1
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => [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]
 => 0 = 1 - 1
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [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]
 => 0 = 1 - 1
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0 = 1 - 1
([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
 => [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]
 => 0 = 1 - 1
([(1,5),(3,4),(4,2),(5,3)],6)
 => [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]
 => 0 = 1 - 1
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 1 - 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 1 - 1
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 1 - 1
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => [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]
 => 0 = 1 - 1
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => [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]
 => 0 = 1 - 1
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 1 - 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001890
(load all 2 compositions to match this statistic)
Mapping
Mp00282: Posets —Dedekind-MacNeille completion⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St001890: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([],1)
 => ([],1)
 => ? = 1
([],2)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
([(0,1)],2)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
([],3)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(1,2)],3)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 1
([(0,1),(0,2)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
([(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ? = 3
([(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ? = 1
([(0,1),(0,2),(0,3)],4)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(3,1)],4)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
([(1,2),(2,3)],4)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ? = 1
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1
([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ? = 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ? = 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ? = 2
([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ? = 3
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ? = 1
([(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)
 => ? = 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ? = 1
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ? = 2
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ? = 2
([(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ? = 4
([(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)
 => ? = 2
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ? = 2
([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ? = 2
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ? = 2
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ? = 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ? = 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ? = 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ? = 3
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)
 => ? = 2
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ? = 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ([(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2)],8)
 => ? = 4
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,2),(7,1),(7,5)],8)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ? = 2
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => ? = 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ? = 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
 => ? = 3
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
 => ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,1),(6,2),(6,3)],8)
 => ? = 2
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)
 => ? = 2
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(7,2),(7,3)],8)
 => ? = 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)
 => ? = 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => ? = 1
([(0,3),(1,4),(4,2)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ? = 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ? = 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)
 => ? = 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => ? = 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => ? = 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ? = 2
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,7),(4,7),(5,7),(7,1),(7,2)],8)
 => ? = 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)
 => ? = 2
Description
The maximum magnitude of the Möbius function of a poset. The '''Möbius function''' of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value μ(x,y) is equal to the signed sum of chains from x to y, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the poset.
Matching statistic: St001327
Mapping
Mp00195: Posets —order ideals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St001327: Graphs ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 50%
Values
([],1)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ([],2)
 => 0 = 1 - 1
([],2)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(2,3)],4)
 => 0 = 1 - 1
([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => ([],3)
 => 0 = 1 - 1
([],3)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
 => ? = 2 - 1
([(1,2)],3)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(2,5),(3,4),(4,5)],6)
 => 0 = 1 - 1
([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([],4)
 => 0 = 1 - 1
([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(3,4)],5)
 => 0 = 1 - 1
([(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
 => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
 => ([(2,8),(2,9),(2,11),(3,6),(3,7),(3,10),(4,5),(4,7),(4,9),(4,10),(4,11),(5,6),(5,8),(5,10),(5,11),(6,7),(6,9),(6,11),(7,8),(7,11),(8,9),(8,10),(9,10),(10,11)],12)
 => ? = 3 - 1
([(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
 => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
 => ([(2,9),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
 => ? = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 2 - 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => 0 = 1 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(4,5)],6)
 => 0 = 1 - 1
([(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)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 1 - 1
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(4,5)],6)
 => 0 = 1 - 1
([(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
 => ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
 => ([(2,9),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,9),(7,9),(8,9)],10)
 => ? = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(4,5)],6)
 => 0 = 1 - 1
([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7)],9)
 => ? = 2 - 1
([(0,3),(1,2)],4)
 => ([(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)
 => ([(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)
 => ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,3),(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
 => ? = 2 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => ([(3,6),(4,5)],7)
 => 1 = 2 - 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([],5)
 => 0 = 1 - 1
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(3,6),(4,5),(5,6)],7)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13)
 => ([(0,5),(1,9),(1,10),(2,6),(2,8),(3,6),(3,7),(4,1),(4,7),(4,8),(5,2),(5,3),(5,4),(6,12),(7,9),(7,12),(8,10),(8,12),(9,11),(10,11),(12,11)],13)
 => ([(3,9),(3,10),(3,12),(4,7),(4,8),(4,11),(5,6),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,11),(6,12),(7,8),(7,10),(7,12),(8,9),(8,12),(9,10),(9,11),(10,11),(11,12)],13)
 => ? = 3 - 1
([(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)
 => ([(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)
 => ([(3,10),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,10),(8,10),(9,10)],11)
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(0,5),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,2),(5,3),(5,4),(6,9),(7,9),(8,9),(9,1)],10)
 => ([(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8)],10)
 => ? = 2 - 1
([(0,3),(0,4),(4,1),(4,2)],5)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ([(0,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,2),(4,3),(4,6),(5,1),(5,4),(6,8),(6,9),(7,10),(8,10),(9,10)],11)
 => ([(3,10),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,10),(8,10),(9,10)],11)
 => ? = 1 - 1
([(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)
 => ([(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)
 => ([(2,11),(3,10),(4,5),(4,7),(4,9),(4,10),(5,7),(5,8),(5,10),(6,7),(6,8),(6,9),(6,10),(7,11),(8,9),(8,11),(9,11),(10,11)],12)
 => ? = 2 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(5,6)],7)
 => 0 = 1 - 1
([(0,3),(0,4),(3,2),(4,1)],5)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
 => ? = 1 - 1
([(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)
 => ([(0,5),(1,7),(2,8),(3,6),(4,3),(4,8),(5,2),(5,4),(6,7),(8,1),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 2 - 1
([(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)
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ([(4,7),(5,6)],8)
 => ? = 2 - 1
([(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16)
 => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,1),(2,9),(2,10),(3,8),(3,12),(4,8),(4,11),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,6),(9,15),(10,7),(10,15),(11,9),(11,13),(12,10),(12,13),(13,15),(15,14)],16)
 => ([(2,12),(2,13),(2,15),(3,10),(3,11),(3,14),(4,5),(4,6),(4,7),(4,10),(4,11),(4,14),(5,8),(5,9),(5,12),(5,13),(5,15),(6,7),(6,9),(6,11),(6,13),(6,14),(6,15),(7,8),(7,10),(7,12),(7,14),(7,15),(8,9),(8,11),(8,13),(8,14),(8,15),(9,10),(9,12),(9,14),(9,15),(10,11),(10,13),(10,15),(11,12),(11,15),(12,13),(12,14),(13,14),(14,15)],16)
 => ? = 4 - 1
([(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,6),(1,9),(2,6),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(5,10),(6,11),(7,10),(8,11),(9,11),(10,8),(10,9)],12)
 => ([(0,3),(0,4),(1,6),(1,9),(2,6),(2,8),(3,7),(4,5),(4,7),(5,1),(5,2),(5,10),(6,11),(7,10),(8,11),(9,11),(10,8),(10,9)],12)
 => ([(2,11),(3,7),(3,11),(4,8),(4,9),(4,10),(5,6),(5,9),(5,10),(6,8),(6,10),(7,8),(7,9),(7,10),(8,9),(8,11),(9,11),(10,11)],12)
 => ? = 2 - 1
([(0,4),(4,1),(4,2),(4,3)],5)
 => ([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10)
 => ([(0,4),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,5),(5,1),(5,2),(5,3),(6,9),(7,9),(8,9)],10)
 => ([(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8)],10)
 => ? = 2 - 1
([(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12)
 => ([(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(3,7),(3,8),(4,6),(4,8),(5,1),(5,9),(6,11),(7,11),(8,5),(8,11),(9,10),(11,9)],12)
 => ([(2,11),(3,7),(3,11),(4,8),(4,9),(4,10),(5,6),(5,9),(5,10),(6,8),(6,10),(7,8),(7,9),(7,10),(8,9),(8,11),(9,11),(10,11)],12)
 => ? = 2 - 1
([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ([(4,7),(5,6)],8)
 => ? = 2 - 1
([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10)
 => ([(0,2),(0,3),(0,4),(2,7),(2,8),(3,6),(3,8),(4,6),(4,7),(5,1),(6,9),(7,9),(8,9),(9,5)],10)
 => ([(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8)],10)
 => ? = 2 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
 => ([(3,4),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,9)],11)
 => ? = 2 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(5,6)],7)
 => 0 = 1 - 1
([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
 => ([(3,10),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,10),(8,10),(9,10)],11)
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(2,9),(2,10),(3,6),(3,8),(4,6),(4,7),(5,2),(5,7),(5,8),(6,11),(7,9),(7,11),(8,10),(8,11),(9,12),(10,12),(11,12),(12,1)],13)
 => ([(0,3),(0,4),(0,5),(2,9),(2,10),(3,6),(3,8),(4,6),(4,7),(5,2),(5,7),(5,8),(6,11),(7,9),(7,11),(8,10),(8,11),(9,12),(10,12),(11,12),(12,1)],13)
 => ([(3,9),(3,10),(3,12),(4,7),(4,8),(4,11),(5,6),(5,8),(5,10),(5,11),(5,12),(6,7),(6,9),(6,11),(6,12),(7,8),(7,10),(7,12),(8,9),(8,12),(9,10),(9,11),(10,11),(11,12)],13)
 => ? = 3 - 1
([(0,4),(1,2),(1,4),(2,3)],5)
 => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)
 => ([(0,3),(0,5),(1,7),(2,8),(3,10),(4,2),(4,6),(5,4),(5,10),(6,7),(6,8),(7,9),(8,9),(10,1),(10,6)],11)
 => ([(2,8),(3,4),(3,10),(4,9),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(8,10),(9,10)],11)
 => ? = 2 - 1
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(0,4),(0,5),(1,6),(3,7),(4,8),(5,1),(5,8),(6,7),(7,2),(8,3),(8,6)],9)
 => ([(3,8),(4,7),(5,6),(6,8),(7,8)],9)
 => ? = 2 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14)
 => ([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14)
 => ([(2,3),(2,8),(2,11),(3,8),(3,10),(4,5),(4,9),(4,13),(5,9),(5,12),(6,9),(6,12),(6,13),(7,8),(7,10),(7,11),(8,9),(8,12),(8,13),(9,10),(9,11),(10,11),(10,12),(10,13),(11,12),(11,13),(12,13)],14)
 => ? = 4 - 1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
 => ([(4,7),(5,6)],8)
 => ? = 2 - 1
([(0,4),(1,2),(1,4),(4,3)],5)
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,1),(5,6),(6,4),(6,8),(8,9),(9,7)],10)
 => ([(2,9),(3,8),(4,5),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ? = 1 - 1
([(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)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(3,4)],5)
 => ([(0,4),(0,5),(1,8),(2,7),(2,9),(3,7),(3,10),(4,6),(5,2),(5,3),(5,6),(6,9),(6,10),(7,11),(9,11),(10,1),(10,11),(11,8)],12)
 => ([(0,4),(0,5),(1,8),(2,7),(2,9),(3,7),(3,10),(4,6),(5,2),(5,3),(5,6),(6,9),(6,10),(7,11),(9,11),(10,1),(10,11),(11,8)],12)
 => ([(2,9),(3,8),(4,6),(4,10),(4,11),(5,7),(5,10),(5,11),(6,7),(6,8),(6,10),(7,9),(7,11),(8,10),(8,11),(9,10),(9,11)],12)
 => ? = 3 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,7),(2,9),(3,7),(3,8),(4,6),(5,2),(5,3),(5,6),(6,8),(6,9),(7,10),(8,10),(9,10),(10,1)],11)
 => ([(0,4),(0,5),(2,7),(2,9),(3,7),(3,8),(4,6),(5,2),(5,3),(5,6),(6,8),(6,9),(7,10),(8,10),(9,10),(10,1)],11)
 => ([(3,10),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,10),(8,10),(9,10)],11)
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,9),(5,9),(6,10),(7,10),(8,10),(9,1),(9,2),(9,3)],11)
 => ([(0,4),(0,5),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,9),(5,9),(6,10),(7,10),(8,10),(9,1),(9,2),(9,3)],11)
 => ([(3,4),(5,8),(5,9),(5,10),(6,7),(6,9),(6,10),(7,8),(7,10),(8,9)],11)
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
 => ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
 => ([(2,9),(3,8),(4,6),(5,7),(6,8),(7,9),(8,9)],10)
 => ? = 1 - 1
([(0,3),(1,2),(1,4),(3,4)],5)
 => ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
 => ([(0,4),(0,5),(1,10),(2,7),(3,8),(4,3),(4,6),(5,1),(5,6),(6,8),(6,10),(8,9),(9,7),(10,2),(10,9)],11)
 => ([(2,8),(3,4),(3,10),(4,9),(5,9),(5,10),(6,7),(6,10),(7,8),(7,9),(8,10),(9,10)],11)
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ([(3,4),(5,8),(6,7),(7,8)],9)
 => ? = 1 - 1
([(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)
 => ([(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)
 => ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 1 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(5,6)],7)
 => 0 = 1 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 1 - 1
([(0,3),(1,4),(4,2)],5)
 => ([(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)
 => ([(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)
 => ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
 => ? = 2 - 1
([(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)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(2,4)],5)
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(4,9),(5,4),(5,6),(6,9),(7,8),(9,1),(9,7)],10)
 => ([(2,9),(3,8),(4,5),(5,9),(6,7),(6,9),(7,8),(8,9)],10)
 => ? = 1 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([],6)
 => 0 = 1 - 1
([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
 => ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
 => ? = 1 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)
 => ? = 1 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(5,6)],7)
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
 => ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
 => ?
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,6),(1,7),(2,7),(3,9),(3,10),(4,8),(4,10),(5,8),(5,9),(6,3),(6,4),(6,5),(8,11),(9,11),(10,11),(11,1),(11,2)],12)
 => ?
 => ?
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
 => ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
 => ?
 => ? = 1 - 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([],7)
 => 0 = 1 - 1
Description
The minimal number of occurrences of the split-pattern in a linear ordering of the vertices of the graph. A graph is a split graph if and only if in any linear ordering of its vertices, there are no three vertices a<b<c such that (a,b) is an edge and (b,c) is not an edge. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.