Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St001199
Mapping
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00228: Dyck paths —reflect parallelogram polyomino⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2,1] => [2,1] => [1,1,0,0]
 => [1,0,1,0]
 => 1
[2,-1] => [2,1] => [1,1,0,0]
 => [1,0,1,0]
 => 1
[-2,1] => [2,1] => [1,1,0,0]
 => [1,0,1,0]
 => 1
[-2,-1] => [2,1] => [1,1,0,0]
 => [1,0,1,0]
 => 1
[1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => 1
[1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => 1
[1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => 1
[1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => 1
[-1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => 1
[-1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => 1
[-1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => 1
[-1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,0]
 => 1
[1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[-1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[-1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[-1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[-1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,0,1,0]
 => 1
[2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[-2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[-2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[-2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[-2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => [1,0,1,1,0,0]
 => 1
[2,3,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 2
[2,3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 2
[2,-3,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 2
[2,-3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 2
[-2,3,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 2
[-2,3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 2
[-2,-3,1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 2
[-2,-3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => 2
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[1,-2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[1,-2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[-1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[-1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[-1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[-1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[-1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
[-1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 1
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001722
Mapping
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001722: Binary words ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 40%
Values
[2,1] => [2,1] => [1,1,0,0]
 => 1100 => 1
[2,-1] => [2,1] => [1,1,0,0]
 => 1100 => 1
[-2,1] => [2,1] => [1,1,0,0]
 => 1100 => 1
[-2,-1] => [2,1] => [1,1,0,0]
 => 1100 => 1
[1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 101010 => 1
[1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => 101010 => 1
[1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 101010 => 1
[1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => 101010 => 1
[-1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 101010 => 1
[-1,2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => 101010 => 1
[-1,-2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 101010 => 1
[-1,-2,-3] => [1,2,3] => [1,0,1,0,1,0]
 => 101010 => 1
[1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => 101100 => 1
[1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => 101100 => 1
[1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
 => 101100 => 1
[1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => 101100 => 1
[-1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => 101100 => 1
[-1,3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => 101100 => 1
[-1,-3,2] => [1,3,2] => [1,0,1,1,0,0]
 => 101100 => 1
[-1,-3,-2] => [1,3,2] => [1,0,1,1,0,0]
 => 101100 => 1
[2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 110010 => 1
[2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => 110010 => 1
[2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 110010 => 1
[2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => 110010 => 1
[-2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 110010 => 1
[-2,1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => 110010 => 1
[-2,-1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 110010 => 1
[-2,-1,-3] => [2,1,3] => [1,1,0,0,1,0]
 => 110010 => 1
[2,3,1] => [2,3,1] => [1,1,0,1,0,0]
 => 110100 => 2
[2,3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => 110100 => 2
[2,-3,1] => [2,3,1] => [1,1,0,1,0,0]
 => 110100 => 2
[2,-3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => 110100 => 2
[-2,3,1] => [2,3,1] => [1,1,0,1,0,0]
 => 110100 => 2
[-2,3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => 110100 => 2
[-2,-3,1] => [2,3,1] => [1,1,0,1,0,0]
 => 110100 => 2
[-2,-3,-1] => [2,3,1] => [1,1,0,1,0,0]
 => 110100 => 2
[1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[1,-2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[1,-2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[-1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[-1,2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[-1,2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[-1,2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[-1,-2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[-1,-2,3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[-1,-2,-3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[-1,-2,-3,-4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 10101010 => ? = 1
[1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[1,2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[1,2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[1,2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[1,-2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[1,-2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[1,-2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[1,-2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[-1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[-1,2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[-1,2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[-1,2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[-1,-2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[-1,-2,4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[-1,-2,-4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[-1,-2,-4,-3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 2
[1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[1,3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[1,3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[1,3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[1,-3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[1,-3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[1,-3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[1,-3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[-1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[-1,3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[-1,3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[-1,3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[-1,-3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[-1,-3,2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[-1,-3,-2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[-1,-3,-2,-4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 10110010 => ? = 1
[1,3,4,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => 10110100 => ? = 2
[1,3,4,-2] => [1,3,4,2] => [1,0,1,1,0,1,0,0]
 => 10110100 => ? = 2
Description
The number of minimal chains with small intervals between a binary word and the top element. A valley in a binary word is a subsequence $01$, or a trailing $0$. A peak is a subsequence $10$ or a trailing $1$. Let $P$ be the lattice on binary words of length $n$, where the covering elements of a word are obtained by replacing a valley with a peak. An interval $[w_1, w_2]$ in $P$ is small if $w_2$ is obtained from $w_1$ by replacing some valleys with peaks. This statistic counts the number of chains $w = w_1 < \dots < w_d = 1\dots 1$ to the top element of minimal length. For example, there are two such chains for the word $0110$: $$ 0110 < 1011 < 1101 < 1110 < 1111 $$ and $$ 0110 < 1010 < 1101 < 1110 < 1111. $$
Matching statistic: St001857
(load all 12 compositions to match this statistic)
Mapping
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00257: Permutations —Alexandersson Kebede⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 40%
Values
[2,1] => [2,1] => [2,1] => [2,1] => 0 = 1 - 1
[2,-1] => [2,1] => [2,1] => [2,1] => 0 = 1 - 1
[-2,1] => [2,1] => [2,1] => [2,1] => 0 = 1 - 1
[-2,-1] => [2,1] => [2,1] => [2,1] => 0 = 1 - 1
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[1,2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[1,-2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[1,-2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[-1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[-1,2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[-1,-2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[-1,-2,-3] => [1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[1,3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0 = 1 - 1
[1,3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0 = 1 - 1
[1,-3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0 = 1 - 1
[1,-3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0 = 1 - 1
[-1,3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0 = 1 - 1
[-1,3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0 = 1 - 1
[-1,-3,2] => [1,3,2] => [3,1,2] => [3,1,2] => 0 = 1 - 1
[-1,-3,-2] => [1,3,2] => [3,1,2] => [3,1,2] => 0 = 1 - 1
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 0 = 1 - 1
[2,1,-3] => [2,1,3] => [2,1,3] => [2,1,3] => 0 = 1 - 1
[2,-1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 0 = 1 - 1
[2,-1,-3] => [2,1,3] => [2,1,3] => [2,1,3] => 0 = 1 - 1
[-2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 0 = 1 - 1
[-2,1,-3] => [2,1,3] => [2,1,3] => [2,1,3] => 0 = 1 - 1
[-2,-1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 0 = 1 - 1
[-2,-1,-3] => [2,1,3] => [2,1,3] => [2,1,3] => 0 = 1 - 1
[2,3,1] => [2,3,1] => [3,2,1] => [3,2,1] => 1 = 2 - 1
[2,3,-1] => [2,3,1] => [3,2,1] => [3,2,1] => 1 = 2 - 1
[2,-3,1] => [2,3,1] => [3,2,1] => [3,2,1] => 1 = 2 - 1
[2,-3,-1] => [2,3,1] => [3,2,1] => [3,2,1] => 1 = 2 - 1
[-2,3,1] => [2,3,1] => [3,2,1] => [3,2,1] => 1 = 2 - 1
[-2,3,-1] => [2,3,1] => [3,2,1] => [3,2,1] => 1 = 2 - 1
[-2,-3,1] => [2,3,1] => [3,2,1] => [3,2,1] => 1 = 2 - 1
[-2,-3,-1] => [2,3,1] => [3,2,1] => [3,2,1] => 1 = 2 - 1
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[-1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[-1,2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[-1,2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[-1,2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[-1,-2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[-1,-2,3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[-1,-2,-3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[-1,-2,-3,-4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => ? = 1 - 1
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[-1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[-1,2,4,-3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[-1,2,-4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[-1,2,-4,-3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[-1,-2,4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[-1,-2,4,-3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[-1,-2,-4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[-1,-2,-4,-3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ? = 2 - 1
[1,3,2,4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[1,3,2,-4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[1,3,-2,4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[1,3,-2,-4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[1,-3,2,4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[1,-3,2,-4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[1,-3,-2,4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[1,-3,-2,-4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[-1,3,2,4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[-1,3,2,-4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[-1,3,-2,4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[-1,3,-2,-4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[-1,-3,2,4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[-1,-3,2,-4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[-1,-3,-2,4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[-1,-3,-2,-4] => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => ? = 1 - 1
[1,3,4,2] => [1,3,4,2] => [3,1,4,2] => [3,1,4,2] => ? = 2 - 1
[1,3,4,-2] => [1,3,4,2] => [3,1,4,2] => [3,1,4,2] => ? = 2 - 1
Description
The number of edges in the reduced word graph of a signed permutation. The reduced word graph of a signed permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move.
Matching statistic: St001880
Mapping
Mp00161: Signed permutations —reverse⟶ Signed permutations
Mp00163: Signed permutations —permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 20%
Values
[2,1] => [1,2] => [1,2] => ([(0,1)],2)
 => ? = 1 + 3
[2,-1] => [-1,2] => [1,2] => ([(0,1)],2)
 => ? = 1 + 3
[-2,1] => [1,-2] => [1,2] => ([(0,1)],2)
 => ? = 1 + 3
[-2,-1] => [-1,-2] => [1,2] => ([(0,1)],2)
 => ? = 1 + 3
[1,2,3] => [3,2,1] => [3,2,1] => ([],3)
 => ? = 1 + 3
[1,2,-3] => [-3,2,1] => [3,2,1] => ([],3)
 => ? = 1 + 3
[1,-2,3] => [3,-2,1] => [3,2,1] => ([],3)
 => ? = 1 + 3
[1,-2,-3] => [-3,-2,1] => [3,2,1] => ([],3)
 => ? = 1 + 3
[-1,2,3] => [3,2,-1] => [3,2,1] => ([],3)
 => ? = 1 + 3
[-1,2,-3] => [-3,2,-1] => [3,2,1] => ([],3)
 => ? = 1 + 3
[-1,-2,3] => [3,-2,-1] => [3,2,1] => ([],3)
 => ? = 1 + 3
[-1,-2,-3] => [-3,-2,-1] => [3,2,1] => ([],3)
 => ? = 1 + 3
[1,3,2] => [2,3,1] => [2,3,1] => ([(1,2)],3)
 => ? = 1 + 3
[1,3,-2] => [-2,3,1] => [2,3,1] => ([(1,2)],3)
 => ? = 1 + 3
[1,-3,2] => [2,-3,1] => [2,3,1] => ([(1,2)],3)
 => ? = 1 + 3
[1,-3,-2] => [-2,-3,1] => [2,3,1] => ([(1,2)],3)
 => ? = 1 + 3
[-1,3,2] => [2,3,-1] => [2,3,1] => ([(1,2)],3)
 => ? = 1 + 3
[-1,3,-2] => [-2,3,-1] => [2,3,1] => ([(1,2)],3)
 => ? = 1 + 3
[-1,-3,2] => [2,-3,-1] => [2,3,1] => ([(1,2)],3)
 => ? = 1 + 3
[-1,-3,-2] => [-2,-3,-1] => [2,3,1] => ([(1,2)],3)
 => ? = 1 + 3
[2,1,3] => [3,1,2] => [3,1,2] => ([(1,2)],3)
 => ? = 1 + 3
[2,1,-3] => [-3,1,2] => [3,1,2] => ([(1,2)],3)
 => ? = 1 + 3
[2,-1,3] => [3,-1,2] => [3,1,2] => ([(1,2)],3)
 => ? = 1 + 3
[2,-1,-3] => [-3,-1,2] => [3,1,2] => ([(1,2)],3)
 => ? = 1 + 3
[-2,1,3] => [3,1,-2] => [3,1,2] => ([(1,2)],3)
 => ? = 1 + 3
[-2,1,-3] => [-3,1,-2] => [3,1,2] => ([(1,2)],3)
 => ? = 1 + 3
[-2,-1,3] => [3,-1,-2] => [3,1,2] => ([(1,2)],3)
 => ? = 1 + 3
[-2,-1,-3] => [-3,-1,-2] => [3,1,2] => ([(1,2)],3)
 => ? = 1 + 3
[2,3,1] => [1,3,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? = 2 + 3
[2,3,-1] => [-1,3,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? = 2 + 3
[2,-3,1] => [1,-3,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? = 2 + 3
[2,-3,-1] => [-1,-3,2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? = 2 + 3
[-2,3,1] => [1,3,-2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? = 2 + 3
[-2,3,-1] => [-1,3,-2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? = 2 + 3
[-2,-3,1] => [1,-3,-2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? = 2 + 3
[-2,-3,-1] => [-1,-3,-2] => [1,3,2] => ([(0,1),(0,2)],3)
 => ? = 2 + 3
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[1,2,3,-4] => [-4,3,2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[1,2,-3,4] => [4,-3,2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[1,2,-3,-4] => [-4,-3,2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[1,-2,3,4] => [4,3,-2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[1,-2,3,-4] => [-4,3,-2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[1,-2,-3,4] => [4,-3,-2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[1,-2,-3,-4] => [-4,-3,-2,1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[-1,2,3,4] => [4,3,2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[-1,2,3,-4] => [-4,3,2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[-1,2,-3,4] => [4,-3,2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[-1,2,-3,-4] => [-4,-3,2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[-1,-2,3,4] => [4,3,-2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[-1,-2,3,-4] => [-4,3,-2,-1] => [4,3,2,1] => ([],4)
 => ? = 1 + 3
[4,2,3,1] => [1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[4,2,3,-1] => [-1,3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[4,2,-3,1] => [1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[4,2,-3,-1] => [-1,-3,2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[4,-2,3,1] => [1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[4,-2,3,-1] => [-1,3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[4,-2,-3,1] => [1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[4,-2,-3,-1] => [-1,-3,-2,4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[-4,2,3,1] => [1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[-4,2,3,-1] => [-1,3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[-4,2,-3,1] => [1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[-4,2,-3,-1] => [-1,-3,2,-4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[-4,-2,3,1] => [1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[-4,-2,3,-1] => [-1,3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[-4,-2,-3,1] => [1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[-4,-2,-3,-1] => [-1,-3,-2,-4] => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4 = 1 + 3
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[4,3,2,-1] => [-1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[4,3,-2,1] => [1,-2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[4,3,-2,-1] => [-1,-2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[4,-3,2,1] => [1,2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[4,-3,2,-1] => [-1,2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[4,-3,-2,1] => [1,-2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[4,-3,-2,-1] => [-1,-2,-3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[-4,3,2,1] => [1,2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[-4,3,2,-1] => [-1,2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[-4,3,-2,1] => [1,-2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[-4,3,-2,-1] => [-1,-2,3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[-4,-3,2,1] => [1,2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[-4,-3,2,-1] => [-1,2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[-4,-3,-2,1] => [1,-2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
[-4,-3,-2,-1] => [-1,-2,-3,-4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 1 + 3
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.