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Your data matches 13 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000359
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St000359: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => [1]
 => [1,0]
 => [1] => 0
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [2,3,1] => 1
[1,0,1,1,0,0]
 => [1,1]
 => [1,1,0,0]
 => [1,2] => 0
[1,1,0,0,1,0]
 => [2]
 => [1,0,1,0]
 => [2,1] => 0
[1,1,0,1,0,0]
 => [1]
 => [1,0]
 => [1] => 0
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => 2
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [3,1,2,4] => 0
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => 2
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [3,2,4,1] => 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [2,1,3] => 0
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 2
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,2,3] => 0
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 2
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [2,3,1] => 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [1,2] => 0
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,0,1,0,1,0]
 => [3,2,1] => 0
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,0,1,0]
 => [2,1] => 0
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0]
 => [1] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,1,2,3,5] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [4,3,1,2,5] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [3,2,1,4] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [2,3,1,4,5] => 1
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => 3
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [4,2,1,3,5] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [3,1,2,4] => 0
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => 2
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [3,2,4,1] => 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [2,1,3] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => 0
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => 4
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => 2
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,2,3] => 0
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => 3
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => 2
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [2,3,1] => 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [1,2] => 0
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => 0
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,0,1,0,1,0]
 => [3,2,1] => 0
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,0,1,0]
 => [2,1] => 0
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0]
 => [1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,5] => 0
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [2,1,3,4,5] => 0
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,1,2,3,5] => 0
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [4,3,1,2,5] => 0
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => 1
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [3,2,1,4] => 0
Description
The number of occurrences of the pattern 23-1. See [[Permutations/#Pattern-avoiding_permutations]] for the definition of the pattern $23\!\!-\!\!1$.
Matching statistic: St000516
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St000516: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => [1]
 => [1,0]
 => [2,1] => 0
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 1
[1,0,1,1,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,3,1] => 0
[1,1,0,0,1,0]
 => [2]
 => [1,0,1,0]
 => [3,1,2] => 0
[1,1,0,1,0,0]
 => [1]
 => [1,0]
 => [2,1] => 0
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => 2
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [2,5,4,1,3] => 0
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [6,1,2,5,3,4] => 2
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [4,3,1,2] => 0
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => 2
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [2,3,4,1] => 0
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => 2
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,3,1] => 0
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 0
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,0,1,0]
 => [3,1,2] => 0
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0]
 => [2,1] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [2,3,6,5,1,4] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [2,6,5,1,3,4] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [5,4,1,2,3] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [5,3,4,1,6,2] => 1
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => 3
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [6,3,5,1,2,4] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [2,5,4,1,3] => 0
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [6,1,2,5,3,4] => 2
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [4,3,1,2] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [5,3,4,1,2] => 0
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [4,1,2,5,6,3] => 4
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => 2
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [2,3,4,1] => 0
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => 3
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => 2
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,3,1] => 0
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 0
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 0
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,0,1,0]
 => [3,1,2] => 0
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0]
 => [2,1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [5,6,1,2,3,4] => 0
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [6,3,4,5,1,2] => 0
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [2,3,6,5,1,4] => 0
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [2,6,5,1,3,4] => 0
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => 1
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [5,4,1,2,3] => 0
Description
The number of stretching pairs of a permutation. This is the number of pairs $(i,j)$ with $\pi(i) < i < j < \pi(j)$.
Matching statistic: St001377
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
St001377: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => [1]
 => [1,0]
 => [1] => 0
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1
[1,0,1,1,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,1] => 0
[1,1,0,0,1,0]
 => [2]
 => [1,0,1,0]
 => [1,2] => 0
[1,1,0,1,0,0]
 => [1]
 => [1,0]
 => [1] => 0
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => 2
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [3,2,4,1] => 0
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => 2
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,3,4,2] => 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [2,3,1] => 0
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 2
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [3,2,1] => 0
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 2
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,1] => 0
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,0,1,0,1,0]
 => [1,2,3] => 0
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,0,1,0]
 => [1,2] => 0
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0]
 => [1] => 0
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [3,5,4,2,1] => 1
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => 3
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [3,4,2,5,1] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [3,2,4,1] => 0
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => 2
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,3,4,2] => 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [2,3,1] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,4,5,3,2] => 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [3,4,2,1] => 0
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => 4
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 2
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [3,2,1] => 0
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => 3
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 2
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,1] => 0
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 0
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,0,1,0,1,0]
 => [1,2,3] => 0
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,0,1,0]
 => [1,2] => 0
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0]
 => [1] => 0
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => 0
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [4,5,3,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => 1
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => 0
Description
The major index minus the number of inversions of a permutation. This is, the difference between [[St000004]] and [[St000018]].
Matching statistic: St000589
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00138: Dyck paths —to noncrossing partition⟶ Set partitions
St000589: Set partitions ⟶ ℤResult quality: 95% ●values known / values provided: 95%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => [1]
 => [1,0]
 => {{1}}
 => ? = 0
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => {{1},{2,3}}
 => 1
[1,0,1,1,0,0]
 => [1,1]
 => [1,1,0,0]
 => {{1,2}}
 => 0
[1,1,0,0,1,0]
 => [2]
 => [1,0,1,0]
 => {{1},{2}}
 => 0
[1,1,0,1,0,0]
 => [1]
 => [1,0]
 => {{1}}
 => ? = 0
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => {{1},{2,5},{3,4}}
 => 2
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => {{1,4},{2,3}}
 => 0
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => {{1},{2},{3,5},{4}}
 => 2
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => {{1},{2,4},{3}}
 => 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => {{1,3},{2}}
 => 0
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => {{1},{2,3,4}}
 => 2
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => {{1,2,3}}
 => 0
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => {{1},{2},{3,4}}
 => 2
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => {{1},{2,3}}
 => 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => {{1,2}}
 => 0
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,0,1,0,1,0]
 => {{1},{2},{3}}
 => 0
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,0,1,0]
 => {{1},{2}}
 => 0
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0]
 => {{1}}
 => ? = 0
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => {{1,5},{2,3,4}}
 => 0
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => {{1,5},{2,3},{4}}
 => 0
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => {{1},{2,5},{3},{4}}
 => 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => {{1,4},{2},{3}}
 => 0
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => {{1,2,4,5},{3}}
 => 1
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => {{1},{2,3,4,5}}
 => 3
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => {{1,2,3,4}}
 => 0
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => {{1,5},{2,4},{3}}
 => 0
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => {{1},{2,5},{3,4}}
 => 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => {{1,4},{2,3}}
 => 0
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => {{1},{2},{3,5},{4}}
 => 2
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => {{1},{2,4},{3}}
 => 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => {{1,3},{2}}
 => 0
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => {{1},{2,3,5},{4}}
 => 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => {{1,2,4},{3}}
 => 0
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => {{1},{2},{3,4,5}}
 => 4
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => {{1},{2,3,4}}
 => 2
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => {{1,2,3}}
 => 0
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => {{1},{2},{3},{4,5}}
 => 3
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => {{1},{2},{3,4}}
 => 2
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => {{1},{2,3}}
 => 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => {{1,2}}
 => 0
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => {{1},{2},{3},{4}}
 => 0
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,0,1,0,1,0]
 => {{1},{2},{3}}
 => 0
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,0,1,0]
 => {{1},{2}}
 => 0
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0]
 => {{1}}
 => ? = 0
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => {{1,5},{2},{3},{4}}
 => 0
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => {{1,2,3,5},{4}}
 => 0
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => {{1,5},{2,3,4}}
 => 0
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => {{1,5},{2,3},{4}}
 => 0
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => {{1},{2,5},{3},{4}}
 => 1
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => {{1,4},{2},{3}}
 => 0
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => {{1,2,3,4,5}}
 => 0
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => {{1,2,4,5},{3}}
 => 1
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => {{1},{2,3,4,5}}
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => {{1,2,3,4}}
 => 0
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1]
 => [1,0]
 => {{1}}
 => ? = 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => {{1}}
 => ? = 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => {{1}}
 => ? = 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => {{1}}
 => ? = 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => {{1}}
 => ? = 0
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => {{1}}
 => ? = 0
Description
The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block.
Matching statistic: St001811
(load all 2 compositions to match this statistic)
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
St001811: Permutations ⟶ ℤResult quality: 95% ●values known / values provided: 95%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => [1]
 => [1,0]
 => [1] => ? = 0
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1
[1,0,1,1,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,1] => 0
[1,1,0,0,1,0]
 => [2]
 => [1,0,1,0]
 => [1,2] => 0
[1,1,0,1,0,0]
 => [1]
 => [1,0]
 => [1] => ? = 0
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => 2
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [3,2,4,1] => 0
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => 2
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,3,4,2] => 1
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [2,3,1] => 0
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 2
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [3,2,1] => 0
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 2
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,1] => 0
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,0,1,0,1,0]
 => [1,2,3] => 0
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,0,1,0]
 => [1,2] => 0
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0]
 => [1] => ? = 0
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => 0
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => 0
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => 0
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [5,2,4,3,1] => 1
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => 3
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 0
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => [4,2,3,5,1] => 0
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => [3,2,4,1] => 0
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => 2
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,3,4,2] => 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => [2,3,1] => 0
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,5,3,4,2] => 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [4,2,3,1] => 0
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => 4
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => [1,4,3,2] => 2
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,1,0,0,0]
 => [3,2,1] => 0
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => 3
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => [1,2,4,3] => 2
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,1,0,0]
 => [1,3,2] => 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,1,0,0]
 => [2,1] => 0
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,2,3,4] => 0
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,0,1,0,1,0]
 => [1,2,3] => 0
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,0,1,0]
 => [1,2] => 0
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0]
 => [1] => ? = 0
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => 0
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => [1,1,1,1,0,1,0,0,0,0]
 => [5,3,4,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => 1
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => 0
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,3,3]
 => [1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => 0
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,3,2]
 => [1,1,1,0,1,1,0,0,0,0]
 => [5,2,4,3,1] => 1
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,2]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1]
 => [1,0]
 => [1] => ? = 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => [1] => ? = 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => [1] => ? = 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => [1] => ? = 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => [1] => ? = 0
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0]
 => [1] => ? = 0
Description
The Castelnuovo-Mumford regularity of a permutation. The ''Castelnuovo-Mumford regularity'' of a permutation $\sigma$ is the ''Castelnuovo-Mumford regularity'' of the ''matrix Schubert variety'' $X_\sigma$. Equivalently, it is the difference between the degrees of the ''Grothendieck polynomial'' and the ''Schubert polynomial'' for $\sigma$. It can be computed by subtracting the ''Coxeter length'' [[St000018]] from the ''Rajchgot index'' [[St001759]].
Matching statistic: St001330
(load all 3 compositions to match this statistic)
Mapping
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 24% ●values known / values provided: 24%●distinct values known / distinct values provided: 60%
Values
[1,0,1,0]
 => [1,0,1,0]
 => [1,1] => ([(0,1)],2)
 => 2 = 0 + 2
[1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 3 = 1 + 2
[1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => [2,1] => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
[1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => [2,1] => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
[1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => [1,2] => ([(1,2)],3)
 => 2 = 0 + 2
[1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
[1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 2 + 2
[1,0,1,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0]
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 1 + 2
[1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 2 + 2
[1,1,0,0,1,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => [2,2] => ([(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 2 + 2
[1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0]
 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 3 = 1 + 2
[1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,0]
 => [2,2] => ([(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,1,1,0,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => [1,3] => ([(2,3)],4)
 => 2 = 0 + 2
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 2
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
[1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 2
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 2
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 2
[1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 2
[1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,3] => ([(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 2
[1,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 2
[1,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => 3 = 1 + 2
[1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,3] => ([(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,4] => ([(3,4)],5)
 => 2 = 0 + 2
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,1,0,0,0,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,1,0,0,0]
 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 2
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,1,0,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4 = 2 + 2
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,1,1,0,0,0,0,0]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,4] => ([(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 2
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,4] => ([(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => [1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
 => [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
 => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
 => [1,1,0,1,0,0,1,1,1,1,0,0,0,0]
 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 3 + 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
 => [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 2 + 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 1 + 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => [3,4] => ([(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 0 + 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => 2 = 0 + 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]
 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => 2 = 0 + 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]
 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => 2 = 0 + 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => 2 = 0 + 2
Description
The hat guessing number of a graph. Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors. Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St001207
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 40%
Values
[1,0,1,0]
 => [1]
 => [1,0,1,0]
 => [3,1,2] => 2 = 0 + 2
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 1 + 2
[1,0,1,1,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 0 + 2
[1,1,0,0,1,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 0 + 2
[1,1,0,1,0,0]
 => [1]
 => [1,0,1,0]
 => [3,1,2] => 2 = 0 + 2
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => ? = 2 + 2
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => ? = 0 + 2
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => ? = 2 + 2
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? = 1 + 2
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? = 0 + 2
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,5,1,3,4] => ? = 2 + 2
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => ? = 0 + 2
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => ? = 2 + 2
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 1 + 2
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 0 + 2
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? = 0 + 2
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 0 + 2
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0,1,0]
 => [3,1,2] => 2 = 0 + 2
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [4,1,2,5,6,3] => ? = 0 + 2
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [5,1,4,2,6,3] => ? = 0 + 2
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => ? = 1 + 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => ? = 0 + 2
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,5,1,3,6,4] => ? = 1 + 2
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,6,1,5,3,4] => ? = 3 + 2
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => ? = 0 + 2
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [5,3,1,2,6,4] => ? = 0 + 2
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => ? = 2 + 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => ? = 0 + 2
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => ? = 2 + 2
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? = 1 + 2
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? = 0 + 2
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [2,3,6,1,4,5] => ? = 2 + 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [2,3,5,1,6,4] => ? = 0 + 2
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => ? = 4 + 2
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,5,1,3,4] => ? = 2 + 2
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => ? = 0 + 2
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => ? = 3 + 2
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => ? = 2 + 2
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 1 + 2
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [2,3,4,6,1,5] => ? = 0 + 2
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? = 0 + 2
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [3,1,2] => 2 = 0 + 2
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [3,1,4,5,6,7,2] => ? = 0 + 2
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,4,1,5,6,7,3] => ? = 0 + 2
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [4,1,2,5,6,3] => ? = 0 + 2
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [5,1,4,2,6,3] => ? = 0 + 2
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => ? = 1 + 2
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => ? = 0 + 2
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [2,3,5,1,6,7,4] => ? = 0 + 2
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,5,1,3,6,4] => ? = 1 + 2
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,6,1,5,3,4] => ? = 3 + 2
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => ? = 0 + 2
[1,1,1,0,1,0,0,1,1,0,0,0]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [5,3,1,2,6,4] => ? = 0 + 2
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => ? = 2 + 2
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => ? = 0 + 2
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => ? = 2 + 2
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? = 1 + 2
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? = 0 + 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [2,3,4,6,1,7,5] => ? = 0 + 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [2,3,6,1,4,5] => ? = 2 + 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [2,3,5,1,6,4] => ? = 0 + 2
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 1 + 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [3,1,2] => 2 = 0 + 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 1 + 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [3,1,2] => 2 = 0 + 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 1 + 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [3,1,2] => 2 = 0 + 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 1 + 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [3,1,2] => 2 = 0 + 2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 0 + 2
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 0 + 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [3,1,2] => 2 = 0 + 2
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => [3,1,2] => 2 = 0 + 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 1 + 2
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 1 + 2
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 0 + 2
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
Matching statistic: St000260
Mapping
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 40%
Values
[1,0,1,0]
 => [1,2] => [1,2] => ([],2)
 => ? = 0 + 1
[1,0,1,0,1,0]
 => [1,2,3] => [1,2,3] => ([],3)
 => ? = 1 + 1
[1,0,1,1,0,0]
 => [1,3,2] => [3,1,2] => ([(0,2),(1,2)],3)
 => 1 = 0 + 1
[1,1,0,0,1,0]
 => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 0 + 1
[1,1,0,1,0,0]
 => [2,3,1] => [1,3,2] => ([(1,2)],3)
 => ? = 0 + 1
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 2 + 1
[1,0,1,0,1,1,0,0]
 => [1,2,4,3] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 1 = 0 + 1
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
[1,0,1,1,0,1,0,0]
 => [1,3,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2 = 1 + 1
[1,0,1,1,1,0,0,0]
 => [1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 0 + 1
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 2 + 1
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 0 + 1
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 2 + 1
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [1,2,4,3] => ([(2,3)],4)
 => ? = 1 + 1
[1,1,0,1,1,0,0,0]
 => [2,4,3,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1 = 0 + 1
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 0 + 1
[1,1,1,0,0,1,0,0]
 => [3,2,4,1] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 0 + 1
[1,1,1,0,1,0,0,0]
 => [3,4,2,1] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,4,2] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,4,5,3,2] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2 = 1 + 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ? = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ? = 2 + 1
[1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,1,0,1,1,0,1,0,0,0]
 => [2,4,5,3,1] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2 = 1 + 1
[1,1,0,1,1,1,0,0,0,0]
 => [2,5,4,3,1] => [5,4,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
 => ? = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => [2,1,4,3,5] => ([(1,4),(2,3)],5)
 => ? = 4 + 1
[1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => [2,1,3,5,4] => ([(1,4),(2,3)],5)
 => ? = 2 + 1
[1,1,1,0,0,1,1,0,0,0]
 => [3,2,5,4,1] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 1
[1,1,1,0,1,0,0,0,1,0]
 => [3,4,2,1,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,1,1,0,1,0,0,1,0,0]
 => [3,4,2,5,1] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ? = 2 + 1
[1,1,1,0,1,0,1,0,0,0]
 => [3,4,5,2,1] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 1 + 1
[1,1,1,0,1,1,0,0,0,0]
 => [3,5,4,2,1] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1 = 0 + 1
[1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 1
[1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 1
[1,1,1,1,0,0,1,0,0,0]
 => [4,3,5,2,1] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 1
[1,1,1,1,0,1,0,0,0,0]
 => [4,5,3,2,1] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 1
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,1,6,5,4,3] => [6,5,1,4,2,3] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,3,6,5,4,1] => [6,5,1,2,4,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,4,6,5,3,1] => [6,2,5,1,4,3] => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,5,6,4,3,1] => [2,6,5,1,4,3] => ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 1 + 1
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,6,5,4,3,1] => [6,5,4,1,3,2] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,2,1,6,5,4] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,2,4,6,5,1] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,5,6,4,1] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,2,6,5,4,1] => [6,1,5,2,4,3] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,1,0,0,1,1,0,0,0]
 => [3,4,2,6,5,1] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [3,4,5,6,2,1] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [3,4,6,5,2,1] => [6,1,2,5,4,3] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,5,4,6,2,1] => [3,1,2,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ? = 2 + 1
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [3,5,6,4,2,1] => [2,6,1,5,4,3] => ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 1 + 1
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [3,6,5,4,2,1] => [6,5,1,4,3,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,3,2,1,6,5] => [3,2,1,6,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ? = 0 + 1
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [4,3,2,5,6,1] => [3,2,1,4,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [4,3,2,6,5,1] => [2,1,6,3,5,4] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [4,3,5,2,6,1] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6)
 => ? = 4 + 1
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [4,3,5,6,2,1] => [2,1,3,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [4,3,6,5,2,1] => [1,6,2,5,4,3] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [4,5,3,2,6,1] => [1,4,3,2,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [4,5,3,6,2,1] => [1,3,2,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [4,5,6,3,2,1] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [4,6,5,3,2,1] => [6,1,5,4,3,2] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1 = 0 + 1
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [5,4,3,2,1,6] => [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [5,4,3,2,6,1] => [4,3,2,1,6,5] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [5,4,3,6,2,1] => [3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ? = 0 + 1
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [5,4,6,3,2,1] => [2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [5,6,4,3,2,1] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [2,7,6,5,4,3,1] => [7,6,5,4,1,3,2] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [3,2,7,6,5,4,1] => [7,6,1,5,2,4,3] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => [3,4,7,6,5,2,1] => [7,6,1,2,5,4,3] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
 => [3,5,7,6,4,2,1] => [7,2,6,1,5,4,3] => ([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
 => [3,6,7,5,4,2,1] => [2,7,6,1,5,4,3] => ([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => [3,7,6,5,4,2,1] => [7,6,5,1,4,3,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [4,3,7,6,5,2,1] => [7,1,6,2,5,4,3] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
 => [4,5,7,6,3,2,1] => [7,1,2,6,5,4,3] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
 => [4,6,7,5,3,2,1] => [2,7,1,6,5,4,3] => ([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 1 + 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [4,7,6,5,3,2,1] => [7,6,1,5,4,3,2] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [5,7,6,4,3,2,1] => [7,1,6,5,4,3,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 1 = 0 + 1
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.
Matching statistic: St000259
Mapping
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00062: Permutations —Lehmer-code to major-code bijection⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 40%
Values
[1,0,1,0]
 => [1,2] => [1,2] => ([],2)
 => ? = 0 + 2
[1,0,1,0,1,0]
 => [1,2,3] => [1,2,3] => ([],3)
 => ? = 1 + 2
[1,0,1,1,0,0]
 => [1,3,2] => [3,1,2] => ([(0,2),(1,2)],3)
 => 2 = 0 + 2
[1,1,0,0,1,0]
 => [2,1,3] => [2,1,3] => ([(1,2)],3)
 => ? = 0 + 2
[1,1,0,1,0,0]
 => [2,3,1] => [1,3,2] => ([(1,2)],3)
 => ? = 0 + 2
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? = 2 + 2
[1,0,1,0,1,1,0,0]
 => [1,2,4,3] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
 => ? = 2 + 2
[1,0,1,1,0,1,0,0]
 => [1,3,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 3 = 1 + 2
[1,0,1,1,1,0,0,0]
 => [1,4,3,2] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 2 + 2
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? = 0 + 2
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 2 + 2
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [1,2,4,3] => ([(2,3)],4)
 => ? = 1 + 2
[1,1,0,1,1,0,0,0]
 => [2,4,3,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2 = 0 + 2
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[1,1,1,0,0,1,0,0]
 => [3,2,4,1] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 0 + 2
[1,1,1,0,1,0,0,0]
 => [3,4,2,1] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 0 + 2
[1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,4,2] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,0,1,1,1,0,1,0,0,0]
 => [1,4,5,3,2] => [2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 3 = 1 + 2
[1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
 => ? = 3 + 2
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ? = 2 + 2
[1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5)
 => ? = 2 + 2
[1,1,0,1,1,0,1,0,0,0]
 => [2,4,5,3,1] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 3 = 1 + 2
[1,1,0,1,1,1,0,0,0,0]
 => [2,5,4,3,1] => [5,4,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
 => ? = 2 + 2
[1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => [2,1,4,3,5] => ([(1,4),(2,3)],5)
 => ? = 4 + 2
[1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => [2,1,3,5,4] => ([(1,4),(2,3)],5)
 => ? = 2 + 2
[1,1,1,0,0,1,1,0,0,0]
 => [3,2,5,4,1] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,1,0,1,0,0,0,1,0]
 => [3,4,2,1,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => ? = 3 + 2
[1,1,1,0,1,0,0,1,0,0]
 => [3,4,2,5,1] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ? = 2 + 2
[1,1,1,0,1,0,1,0,0,0]
 => [3,4,5,2,1] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 1 + 2
[1,1,1,0,1,1,0,0,0,0]
 => [3,5,4,2,1] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2 = 0 + 2
[1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,1,1,0,0,1,0,0,0]
 => [4,3,5,2,1] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,1,1,1,0,1,0,0,0,0]
 => [4,5,3,2,1] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,6,5,4,3,2] => [6,5,4,3,1,2] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,1,6,5,4,3] => [6,5,1,4,2,3] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,3,6,5,4,1] => [6,5,1,2,4,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,4,6,5,3,1] => [6,2,5,1,4,3] => ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,5,6,4,3,1] => [2,6,5,1,4,3] => ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,6,5,4,3,1] => [6,5,4,1,3,2] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,2,1,6,5,4] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,2,4,6,5,1] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,5,6,4,1] => [1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ? = 3 + 2
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,2,6,5,4,1] => [6,1,5,2,4,3] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,1,0,0,1,1,0,0,0]
 => [3,4,2,6,5,1] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [3,4,5,6,2,1] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [3,4,6,5,2,1] => [6,1,2,5,4,3] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,5,4,6,2,1] => [3,1,2,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ? = 2 + 2
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [3,5,6,4,2,1] => [2,6,1,5,4,3] => ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3 = 1 + 2
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [3,6,5,4,2,1] => [6,5,1,4,3,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,3,2,1,6,5] => [3,2,1,6,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ? = 0 + 2
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [4,3,2,5,6,1] => [3,2,1,4,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [4,3,2,6,5,1] => [2,1,6,3,5,4] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [4,3,5,2,6,1] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6)
 => ? = 4 + 2
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [4,3,5,6,2,1] => [2,1,3,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [4,3,6,5,2,1] => [1,6,2,5,4,3] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [4,5,3,2,6,1] => [1,4,3,2,6,5] => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 2
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [4,5,3,6,2,1] => [1,3,2,6,5,4] => ([(1,2),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 2
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [4,5,6,3,2,1] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [4,6,5,3,2,1] => [6,1,5,4,3,2] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [5,4,3,2,1,6] => [5,4,3,2,1,6] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [5,4,3,2,6,1] => [4,3,2,1,6,5] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [5,4,3,6,2,1] => [3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
 => ? = 0 + 2
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [5,4,6,3,2,1] => [2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [5,6,4,3,2,1] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [2,7,6,5,4,3,1] => [7,6,5,4,1,3,2] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [3,2,7,6,5,4,1] => [7,6,1,5,2,4,3] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => [3,4,7,6,5,2,1] => [7,6,1,2,5,4,3] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
 => [3,5,7,6,4,2,1] => [7,2,6,1,5,4,3] => ([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
 => [3,6,7,5,4,2,1] => [2,7,6,1,5,4,3] => ([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => [3,7,6,5,4,2,1] => [7,6,5,1,4,3,2] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [4,3,7,6,5,2,1] => [7,1,6,2,5,4,3] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
 => [4,5,7,6,3,2,1] => [7,1,2,6,5,4,3] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
 => [4,6,7,5,3,2,1] => [2,7,1,6,5,4,3] => ([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 3 = 1 + 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [4,7,6,5,3,2,1] => [7,6,1,5,4,3,2] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
 => [5,7,6,4,3,2,1] => [7,1,6,5,4,3,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => 2 = 0 + 2
Description
The diameter of a connected graph. This is the greatest distance between any pair of vertices.
Matching statistic: St001876
Mapping
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 20%
Values
[1,0,1,0]
 => [1,1,0,0]
 => ([],2)
 => ([],1)
 => ? = 0
[1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ([],3)
 => ([],1)
 => ? = 1
[1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => ([(1,2)],3)
 => ([(0,1)],2)
 => ? = 0
[1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => ([(0,1),(0,2)],3)
 => ([],1)
 => ? = 0
[1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => ([(0,2),(1,2)],3)
 => ([],1)
 => ? = 0
[1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ([],4)
 => ([],1)
 => ? = 2
[1,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => ([(2,3)],4)
 => ([(0,1)],2)
 => ? = 0
[1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => ([(1,2),(1,3)],4)
 => ([],1)
 => ? = 2
[1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => ([(1,3),(2,3)],4)
 => ([],1)
 => ? = 1
[1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3)],4)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3)],4)
 => ([],1)
 => ? = 2
[1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(3,1)],4)
 => ([(0,1)],2)
 => ? = 0
[1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0]
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1)],2)
 => ? = 2
[1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? = 1
[1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? = 0
[1,1,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0]
 => ([(0,3),(3,1),(3,2)],4)
 => ([],1)
 => ? = 0
[1,1,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([],1)
 => ? = 0
[1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0]
 => ([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ? = 0
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(2,1)],3)
 => 0
[1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ? = 0
[1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([],1)
 => ? = 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ([(0,2),(0,3),(0,4),(4,1)],5)
 => ([(0,1)],2)
 => ? = 1
[1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 3
[1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? = 2
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? = 0
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([],1)
 => ? = 2
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ? = 1
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,0,1,0]
 => ([(0,4),(4,1),(4,2),(4,3)],5)
 => ([],1)
 => ? = 2
[1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,1)],2)
 => ? = 0
[1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1)],2)
 => ? = 4
[1,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? = 2
[1,1,1,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,1)],2)
 => ? = 0
[1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => ([(0,4),(1,4),(4,2),(4,3)],5)
 => ([(0,1)],2)
 => ? = 3
[1,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
 => ([(0,1)],2)
 => ? = 2
[1,1,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ? = 1
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ? = 0
[1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => ([(0,3),(3,4),(4,1),(4,2)],5)
 => ([],1)
 => ? = 0
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([],1)
 => ? = 0
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([],1)
 => ? = 0
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ? = 0
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => ([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
 => ([(0,1)],2)
 => ? = 0
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,1,0,0,0]
 => ([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)
 => ([],1)
 => ? = 1
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => ([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)
 => ([(0,1)],2)
 => ? = 1
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([],1)
 => ? = 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,0,1,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => ([],1)
 => ? = 2
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6)
 => ([(0,1)],2)
 => ? = 0
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => ([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => ([],1)
 => ? = 2
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
 => ([],1)
 => ? = 1
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => ([(0,1)],2)
 => ? = 0
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => ([],1)
 => ? = 2
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,1)],2)
 => ? = 0
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => ([(0,1)],2)
 => ? = 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
 => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => ([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)
 => ([(0,3),(2,1),(3,2)],4)
 => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => ([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,2),(2,1)],3)
 => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,2),(2,1)],3)
 => 0
Description
The number of 2-regular simple modules in the incidence algebra of the lattice.
The following 3 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001877Number of indecomposable injective modules with projective dimension 2. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001964The interval resolution global dimension of a poset.