Your data matches 48 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000075
(load all 60 compositions to match this statistic)
Mapping
St000075: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => 1
[[1],[2]]
 => 1
[[1,2,3]]
 => 1
[[1,3],[2]]
 => 2
[[1,2],[3]]
 => 2
[[1],[2],[3]]
 => 1
[[1,2,3,4]]
 => 1
[[1,3,4],[2]]
 => 3
[[1,2,4],[3]]
 => 3
[[1,2,3],[4]]
 => 3
[[1,3],[2,4]]
 => 2
[[1,2],[3,4]]
 => 2
[[1,4],[2],[3]]
 => 3
[[1,3],[2],[4]]
 => 3
[[1,2],[3],[4]]
 => 3
[[1],[2],[3],[4]]
 => 1
Description
The orbit size of a standard tableau under promotion.
Matching statistic: St000003
(load all 2 compositions to match this statistic)
Mapping
Mp00083: Standard tableaux —shape⟶ Integer partitions
St000003: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [2]
 => 1
[[1],[2]]
 => [1,1]
 => 1
[[1,2,3]]
 => [3]
 => 1
[[1,3],[2]]
 => [2,1]
 => 2
[[1,2],[3]]
 => [2,1]
 => 2
[[1],[2],[3]]
 => [1,1,1]
 => 1
[[1,2,3,4]]
 => [4]
 => 1
[[1,3,4],[2]]
 => [3,1]
 => 3
[[1,2,4],[3]]
 => [3,1]
 => 3
[[1,2,3],[4]]
 => [3,1]
 => 3
[[1,3],[2,4]]
 => [2,2]
 => 2
[[1,2],[3,4]]
 => [2,2]
 => 2
[[1,4],[2],[3]]
 => [2,1,1]
 => 3
[[1,3],[2],[4]]
 => [2,1,1]
 => 3
[[1,2],[3],[4]]
 => [2,1,1]
 => 3
[[1],[2],[3],[4]]
 => [1,1,1,1]
 => 1
Description
The number of [[/StandardTableaux|standard Young tableaux]] of the partition.
Matching statistic: St001686
(load all 22 compositions to match this statistic)
Mapping
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St001686: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [[2,0],[1]]
 => 1
[[1],[2]]
 => [[1,1],[1]]
 => 1
[[1,2,3]]
 => [[3,0,0],[2,0],[1]]
 => 1
[[1,3],[2]]
 => [[2,1,0],[1,1],[1]]
 => 2
[[1,2],[3]]
 => [[2,1,0],[2,0],[1]]
 => 2
[[1],[2],[3]]
 => [[1,1,1],[1,1],[1]]
 => 1
[[1,2,3,4]]
 => [[4,0,0,0],[3,0,0],[2,0],[1]]
 => 1
[[1,3,4],[2]]
 => [[3,1,0,0],[2,1,0],[1,1],[1]]
 => 3
[[1,2,4],[3]]
 => [[3,1,0,0],[2,1,0],[2,0],[1]]
 => 3
[[1,2,3],[4]]
 => [[3,1,0,0],[3,0,0],[2,0],[1]]
 => 3
[[1,3],[2,4]]
 => [[2,2,0,0],[2,1,0],[1,1],[1]]
 => 2
[[1,2],[3,4]]
 => [[2,2,0,0],[2,1,0],[2,0],[1]]
 => 2
[[1,4],[2],[3]]
 => [[2,1,1,0],[1,1,1],[1,1],[1]]
 => 3
[[1,3],[2],[4]]
 => [[2,1,1,0],[2,1,0],[1,1],[1]]
 => 3
[[1,2],[3],[4]]
 => [[2,1,1,0],[2,1,0],[2,0],[1]]
 => 3
[[1],[2],[3],[4]]
 => [[1,1,1,1],[1,1,1],[1,1],[1]]
 => 1
Description
The order of promotion on a Gelfand-Tsetlin pattern.
Matching statistic: St001780
(load all 2 compositions to match this statistic)
Mapping
Mp00083: Standard tableaux —shape⟶ Integer partitions
St001780: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [2]
 => 1
[[1],[2]]
 => [1,1]
 => 1
[[1,2,3]]
 => [3]
 => 1
[[1,3],[2]]
 => [2,1]
 => 2
[[1,2],[3]]
 => [2,1]
 => 2
[[1],[2],[3]]
 => [1,1,1]
 => 1
[[1,2,3,4]]
 => [4]
 => 1
[[1,3,4],[2]]
 => [3,1]
 => 3
[[1,2,4],[3]]
 => [3,1]
 => 3
[[1,2,3],[4]]
 => [3,1]
 => 3
[[1,3],[2,4]]
 => [2,2]
 => 2
[[1,2],[3,4]]
 => [2,2]
 => 2
[[1,4],[2],[3]]
 => [2,1,1]
 => 3
[[1,3],[2],[4]]
 => [2,1,1]
 => 3
[[1,2],[3],[4]]
 => [2,1,1]
 => 3
[[1],[2],[3],[4]]
 => [1,1,1,1]
 => 1
Description
The order of promotion on the set of standard tableaux of given shape.
Matching statistic: St000626
(load all 5 compositions to match this statistic)
Mapping
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
St000626: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [1,2] => 0 => 1
[[1],[2]]
 => [2,1] => 1 => 1
[[1,2,3]]
 => [1,2,3] => 00 => 1
[[1,3],[2]]
 => [2,1,3] => 10 => 2
[[1,2],[3]]
 => [3,1,2] => 10 => 2
[[1],[2],[3]]
 => [3,2,1] => 11 => 1
[[1,2,3,4]]
 => [1,2,3,4] => 000 => 1
[[1,3,4],[2]]
 => [2,1,3,4] => 100 => 3
[[1,2,4],[3]]
 => [3,1,2,4] => 100 => 3
[[1,2,3],[4]]
 => [4,1,2,3] => 100 => 3
[[1,3],[2,4]]
 => [2,4,1,3] => 010 => 2
[[1,2],[3,4]]
 => [3,4,1,2] => 010 => 2
[[1,4],[2],[3]]
 => [3,2,1,4] => 110 => 3
[[1,3],[2],[4]]
 => [4,2,1,3] => 110 => 3
[[1,2],[3],[4]]
 => [4,3,1,2] => 110 => 3
[[1],[2],[3],[4]]
 => [4,3,2,1] => 111 => 1
Description
The minimal period of a binary word. This is the smallest natural number $p$ such that $w_i=w_{i+p}$ for all $i\in\{1,\dots,|w|-p\}$.
Matching statistic: St001595
(load all 3 compositions to match this statistic)
Mapping
Mp00083: Standard tableaux —shape⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001595: Skew partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [2]
 => [[2],[]]
 => 1
[[1],[2]]
 => [1,1]
 => [[1,1],[]]
 => 1
[[1,2,3]]
 => [3]
 => [[3],[]]
 => 1
[[1,3],[2]]
 => [2,1]
 => [[2,1],[]]
 => 2
[[1,2],[3]]
 => [2,1]
 => [[2,1],[]]
 => 2
[[1],[2],[3]]
 => [1,1,1]
 => [[1,1,1],[]]
 => 1
[[1,2,3,4]]
 => [4]
 => [[4],[]]
 => 1
[[1,3,4],[2]]
 => [3,1]
 => [[3,1],[]]
 => 3
[[1,2,4],[3]]
 => [3,1]
 => [[3,1],[]]
 => 3
[[1,2,3],[4]]
 => [3,1]
 => [[3,1],[]]
 => 3
[[1,3],[2,4]]
 => [2,2]
 => [[2,2],[]]
 => 2
[[1,2],[3,4]]
 => [2,2]
 => [[2,2],[]]
 => 2
[[1,4],[2],[3]]
 => [2,1,1]
 => [[2,1,1],[]]
 => 3
[[1,3],[2],[4]]
 => [2,1,1]
 => [[2,1,1],[]]
 => 3
[[1,2],[3],[4]]
 => [2,1,1]
 => [[2,1,1],[]]
 => 3
[[1],[2],[3],[4]]
 => [1,1,1,1]
 => [[1,1,1,1],[]]
 => 1
Description
The number of standard Young tableaux of the skew partition.
Matching statistic: St001929
(load all 6 compositions to match this statistic)
Mapping
Mp00083: Standard tableaux —shape⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001929: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [2]
 => [1,0,1,0]
 => 1
[[1],[2]]
 => [1,1]
 => [1,1,0,0]
 => 1
[[1,2,3]]
 => [3]
 => [1,0,1,0,1,0]
 => 1
[[1,3],[2]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[[1,2],[3]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[[1],[2],[3]]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 1
[[1,2,3,4]]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => 1
[[1,3,4],[2]]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 3
[[1,2,4],[3]]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 3
[[1,2,3],[4]]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 3
[[1,3],[2,4]]
 => [2,2]
 => [1,1,1,0,0,0]
 => 2
[[1,2],[3,4]]
 => [2,2]
 => [1,1,1,0,0,0]
 => 2
[[1,4],[2],[3]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 3
[[1,3],[2],[4]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 3
[[1,2],[3],[4]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 3
[[1],[2],[3],[4]]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 1
Description
The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path.
Matching statistic: St000057
(load all 2 compositions to match this statistic)
Mapping
Mp00083: Standard tableaux —shape⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
St000057: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [2]
 => [[1,2]]
 => 0 = 1 - 1
[[1],[2]]
 => [1,1]
 => [[1],[2]]
 => 0 = 1 - 1
[[1,2,3]]
 => [3]
 => [[1,2,3]]
 => 0 = 1 - 1
[[1,3],[2]]
 => [2,1]
 => [[1,2],[3]]
 => 1 = 2 - 1
[[1,2],[3]]
 => [2,1]
 => [[1,2],[3]]
 => 1 = 2 - 1
[[1],[2],[3]]
 => [1,1,1]
 => [[1],[2],[3]]
 => 0 = 1 - 1
[[1,2,3,4]]
 => [4]
 => [[1,2,3,4]]
 => 0 = 1 - 1
[[1,3,4],[2]]
 => [3,1]
 => [[1,2,3],[4]]
 => 2 = 3 - 1
[[1,2,4],[3]]
 => [3,1]
 => [[1,2,3],[4]]
 => 2 = 3 - 1
[[1,2,3],[4]]
 => [3,1]
 => [[1,2,3],[4]]
 => 2 = 3 - 1
[[1,3],[2,4]]
 => [2,2]
 => [[1,2],[3,4]]
 => 1 = 2 - 1
[[1,2],[3,4]]
 => [2,2]
 => [[1,2],[3,4]]
 => 1 = 2 - 1
[[1,4],[2],[3]]
 => [2,1,1]
 => [[1,2],[3],[4]]
 => 2 = 3 - 1
[[1,3],[2],[4]]
 => [2,1,1]
 => [[1,2],[3],[4]]
 => 2 = 3 - 1
[[1,2],[3],[4]]
 => [2,1,1]
 => [[1,2],[3],[4]]
 => 2 = 3 - 1
[[1],[2],[3],[4]]
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => 0 = 1 - 1
Description
The Shynar inversion number of a standard tableau. Shynar's inversion number is the number of inversion pairs in a standard Young tableau, where an inversion pair is defined as a pair of integers (x,y) such that y > x and y appears strictly southwest of x in the tableau.
Matching statistic: St000293
(load all 3 compositions to match this statistic)
Mapping
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
St000293: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [1,2] => 0 => 0 = 1 - 1
[[1],[2]]
 => [2,1] => 1 => 0 = 1 - 1
[[1,2,3]]
 => [1,2,3] => 00 => 0 = 1 - 1
[[1,3],[2]]
 => [2,1,3] => 10 => 1 = 2 - 1
[[1,2],[3]]
 => [3,1,2] => 10 => 1 = 2 - 1
[[1],[2],[3]]
 => [3,2,1] => 11 => 0 = 1 - 1
[[1,2,3,4]]
 => [1,2,3,4] => 000 => 0 = 1 - 1
[[1,3,4],[2]]
 => [2,1,3,4] => 100 => 2 = 3 - 1
[[1,2,4],[3]]
 => [3,1,2,4] => 100 => 2 = 3 - 1
[[1,2,3],[4]]
 => [4,1,2,3] => 100 => 2 = 3 - 1
[[1,3],[2,4]]
 => [2,4,1,3] => 010 => 1 = 2 - 1
[[1,2],[3,4]]
 => [3,4,1,2] => 010 => 1 = 2 - 1
[[1,4],[2],[3]]
 => [3,2,1,4] => 110 => 2 = 3 - 1
[[1,3],[2],[4]]
 => [4,2,1,3] => 110 => 2 = 3 - 1
[[1,2],[3],[4]]
 => [4,3,1,2] => 110 => 2 = 3 - 1
[[1],[2],[3],[4]]
 => [4,3,2,1] => 111 => 0 = 1 - 1
Description
The number of inversions of a binary word.
Matching statistic: St001436
(load all 3 compositions to match this statistic)
Mapping
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
St001436: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1,2]]
 => [1,2] => 0 => 0 = 1 - 1
[[1],[2]]
 => [2,1] => 1 => 0 = 1 - 1
[[1,2,3]]
 => [1,2,3] => 00 => 0 = 1 - 1
[[1,3],[2]]
 => [2,1,3] => 10 => 1 = 2 - 1
[[1,2],[3]]
 => [3,1,2] => 10 => 1 = 2 - 1
[[1],[2],[3]]
 => [3,2,1] => 11 => 0 = 1 - 1
[[1,2,3,4]]
 => [1,2,3,4] => 000 => 0 = 1 - 1
[[1,3,4],[2]]
 => [2,1,3,4] => 100 => 2 = 3 - 1
[[1,2,4],[3]]
 => [3,1,2,4] => 100 => 2 = 3 - 1
[[1,2,3],[4]]
 => [4,1,2,3] => 100 => 2 = 3 - 1
[[1,3],[2,4]]
 => [2,4,1,3] => 010 => 1 = 2 - 1
[[1,2],[3,4]]
 => [3,4,1,2] => 010 => 1 = 2 - 1
[[1,4],[2],[3]]
 => [3,2,1,4] => 110 => 2 = 3 - 1
[[1,3],[2],[4]]
 => [4,2,1,3] => 110 => 2 = 3 - 1
[[1,2],[3],[4]]
 => [4,3,1,2] => 110 => 2 = 3 - 1
[[1],[2],[3],[4]]
 => [4,3,2,1] => 111 => 0 = 1 - 1
Description
The index of a given binary word in the lex-order among all its cyclic shifts.
The following 38 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000001The number of reduced words for a permutation. St000047The number of standard immaculate tableaux of a given shape. St000100The number of linear extensions of a poset. St000525The number of posets with the same zeta polynomial. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001268The size of the largest ordinal summand in the poset. St001313The number of Dyck paths above the lattice path given by a binary word. St001415The length of the longest palindromic prefix of a binary word. St001779The order of promotion on the set of linear extensions of a poset. St000222The number of alignments in the permutation. St000290The major index of a binary word. St000369The dinv deficit of a Dyck path. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000427The number of occurrences of the pattern 123 or of the pattern 231 in a permutation. St000433The number of occurrences of the pattern 132 or of the pattern 321 in a permutation. St000457The number of occurrences of one of the patterns 132, 213 or 321 in a permutation. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000682The Grundy value of Welter's game on a binary word. St000747A variant of the major index of a set partition. St000849The number of 1/3-balanced pairs in a poset. St001397Number of pairs of incomparable elements in a finite poset. St001398Number of subsets of size 3 of elements in a poset that form a "v". St001485The modular major index of a binary word. St001856The number of edges in the reduced word graph of a permutation. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St001623The number of doubly irreducible elements of a lattice. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000259The diameter of a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001171The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$. St000260The radius of a connected graph. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001498The normalised height of a Nakayama algebra with magnitude 1.