Your data matches 153 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001595
Mapping
St001595: Skew partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => 1
[[2],[]]
 => 1
[[1,1],[]]
 => 1
[[2,1],[1]]
 => 2
[[3],[]]
 => 1
[[2,1],[]]
 => 2
[[3,1],[1]]
 => 3
[[2,2],[1]]
 => 2
[[3,2],[2]]
 => 3
[[1,1,1],[]]
 => 1
[[2,2,1],[1,1]]
 => 3
[[2,1,1],[1]]
 => 3
[[3,2,1],[2,1]]
 => 6
Description
The number of standard Young tableaux of the skew partition.
Matching statistic: St000208
Mapping
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St000208: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => ([],1)
 => [1]
 => 1
[[2],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[1,1],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[2,1],[1]]
 => ([],2)
 => [2]
 => 2
[[3],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,1],[]]
 => ([(0,1),(0,2)],3)
 => [2]
 => 2
[[3,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => [2]
 => 2
[[3,2],[2]]
 => ([(1,2)],3)
 => [3]
 => 3
[[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,2,1],[1,1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,1,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[3,2,1],[2,1]]
 => ([],3)
 => [3,3]
 => 6
Description
Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. Given $\lambda$ count how many ''integer partitions'' $w$ (weight) there are, such that $P_{\lambda,w}$ is integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has only integer lattice points as vertices. See also [[St000205]], [[St000206]] and [[St000207]].
Matching statistic: St000228
(load all 2 compositions to match this statistic)
Mapping
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St000228: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => ([],1)
 => [1]
 => 1
[[2],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[1,1],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[2,1],[1]]
 => ([],2)
 => [2]
 => 2
[[3],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,1],[]]
 => ([(0,1),(0,2)],3)
 => [2]
 => 2
[[3,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => [2]
 => 2
[[3,2],[2]]
 => ([(1,2)],3)
 => [3]
 => 3
[[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,2,1],[1,1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,1,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[3,2,1],[2,1]]
 => ([],3)
 => [3,3]
 => 6
Description
The size of a partition. This statistic is the constant statistic of the level sets.
Matching statistic: St000345
Mapping
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St000345: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => ([],1)
 => [1]
 => 1
[[2],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[1,1],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[2,1],[1]]
 => ([],2)
 => [2]
 => 2
[[3],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,1],[]]
 => ([(0,1),(0,2)],3)
 => [2]
 => 2
[[3,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => [2]
 => 2
[[3,2],[2]]
 => ([(1,2)],3)
 => [3]
 => 3
[[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,2,1],[1,1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,1,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[3,2,1],[2,1]]
 => ([],3)
 => [3,3]
 => 6
Description
The number of refinements of a partition. A partition $\lambda$ refines a partition $\mu$ if the parts of $\mu$ can be subdivided to obtain the parts of $\lambda$.
Matching statistic: St000531
(load all 2 compositions to match this statistic)
Mapping
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St000531: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => ([],1)
 => [1]
 => 1
[[2],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[1,1],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[2,1],[1]]
 => ([],2)
 => [2]
 => 2
[[3],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,1],[]]
 => ([(0,1),(0,2)],3)
 => [2]
 => 2
[[3,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => [2]
 => 2
[[3,2],[2]]
 => ([(1,2)],3)
 => [3]
 => 3
[[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,2,1],[1,1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,1,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[3,2,1],[2,1]]
 => ([],3)
 => [3,3]
 => 6
Description
The leading coefficient of the rook polynomial of an integer partition. Let $m$ be the minimum of the number of parts and the size of the first part of an integer partition $\lambda$. Then this statistic yields the number of ways to place $m$ non-attacking rooks on the Ferrers board of $\lambda$.
Matching statistic: St001389
Mapping
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St001389: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => ([],1)
 => [1]
 => 1
[[2],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[1,1],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[2,1],[1]]
 => ([],2)
 => [2]
 => 2
[[3],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,1],[]]
 => ([(0,1),(0,2)],3)
 => [2]
 => 2
[[3,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => [2]
 => 2
[[3,2],[2]]
 => ([(1,2)],3)
 => [3]
 => 3
[[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,2,1],[1,1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,1,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[3,2,1],[2,1]]
 => ([],3)
 => [3,3]
 => 6
Description
The number of partitions of the same length below the given integer partition. For a partition $\lambda_1 \geq \dots \lambda_k > 0$, this number is $$ \det\left( \binom{\lambda_{k+1-i}}{j-i+1} \right)_{1 \le i,j \le k}.$$
Matching statistic: St001659
(load all 2 compositions to match this statistic)
Mapping
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00307: Posets —promotion cycle type⟶ Integer partitions
St001659: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => ([],1)
 => [1]
 => 1
[[2],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[1,1],[]]
 => ([(0,1)],2)
 => [1]
 => 1
[[2,1],[1]]
 => ([],2)
 => [2]
 => 2
[[3],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,1],[]]
 => ([(0,1),(0,2)],3)
 => [2]
 => 2
[[3,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => [2]
 => 2
[[3,2],[2]]
 => ([(1,2)],3)
 => [3]
 => 3
[[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => [1]
 => 1
[[2,2,1],[1,1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[2,1,1],[1]]
 => ([(1,2)],3)
 => [3]
 => 3
[[3,2,1],[2,1]]
 => ([],3)
 => [3,3]
 => 6
Description
The number of ways to place as many non-attacking rooks as possible on a Ferrers board.
Matching statistic: St000071
Mapping
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000071: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => ([],1)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
[[2],[]]
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[[1,1],[]]
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[[2,1],[1]]
 => ([],2)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[[3],[]]
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[[2,1],[]]
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 2
[[3,1],[1]]
 => ([(1,2)],3)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 3
[[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
[[3,2],[2]]
 => ([(1,2)],3)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 3
[[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[[2,2,1],[1,1]]
 => ([(1,2)],3)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 3
[[2,1,1],[1]]
 => ([(1,2)],3)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 3
[[3,2,1],[2,1]]
 => ([],3)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => 6
Description
The number of maximal chains in a poset.
Matching statistic: St000909
Mapping
Mp00185: Skew partitions —cell poset⟶ Posets
Mp00195: Posets —order ideals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St000909: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => ([],1)
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
[[2],[]]
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[[1,1],[]]
 => ([(0,1)],2)
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 1
[[2,1],[1]]
 => ([],2)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[[3],[]]
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[[2,1],[]]
 => ([(0,1),(0,2)],3)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 2
[[3,1],[1]]
 => ([(1,2)],3)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 3
[[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 2
[[3,2],[2]]
 => ([(1,2)],3)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 3
[[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[[2,2,1],[1,1]]
 => ([(1,2)],3)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 3
[[2,1,1],[1]]
 => ([(1,2)],3)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 3
[[3,2,1],[2,1]]
 => ([],3)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
 => 6
Description
The number of maximal chains of maximal size in a poset.
Matching statistic: St000100
(load all 2 compositions to match this statistic)
Mapping
Mp00185: Skew partitions —cell poset⟶ Posets
St000100: Posets ⟶ ℤResult quality: 92% ●values known / values provided: 92%●distinct values known / distinct values provided: 100%
Values
[[1],[]]
 => ([],1)
 => ? = 1
[[2],[]]
 => ([(0,1)],2)
 => 1
[[1,1],[]]
 => ([(0,1)],2)
 => 1
[[2,1],[1]]
 => ([],2)
 => 2
[[3],[]]
 => ([(0,2),(2,1)],3)
 => 1
[[2,1],[]]
 => ([(0,1),(0,2)],3)
 => 2
[[3,1],[1]]
 => ([(1,2)],3)
 => 3
[[2,2],[1]]
 => ([(0,2),(1,2)],3)
 => 2
[[3,2],[2]]
 => ([(1,2)],3)
 => 3
[[1,1,1],[]]
 => ([(0,2),(2,1)],3)
 => 1
[[2,2,1],[1,1]]
 => ([(1,2)],3)
 => 3
[[2,1,1],[1]]
 => ([(1,2)],3)
 => 3
[[3,2,1],[2,1]]
 => ([],3)
 => 6
Description
The number of linear extensions of a poset.
The following 143 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000910The number of maximal chains of minimal length in a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001808The box weight or horizontal decoration of a Dyck path. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001877Number of indecomposable injective modules with projective dimension 2. St001118The acyclic chromatic index of a graph. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000812The sum of the entries in the column specified by the partition of the change of basis matrix from complete homogeneous symmetric functions to monomial symmetric functions. St000867The sum of the hook lengths in the first row of an integer partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000454The largest eigenvalue of a graph if it is integral. St001686The order of promotion on a Gelfand-Tsetlin pattern. St000456The monochromatic index of a connected graph. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000815The number of semistandard Young tableaux of partition weight of given shape. St001816Eigenvalues of the top-to-random operator acting on a simple module. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000259The diameter of a connected graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000467The hyper-Wiener index of a connected graph. St001330The hat guessing number of a graph. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St001060The distinguishing index of a graph. St000420The number of Dyck paths that are weakly above a Dyck path. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000762The sum of the positions of the weak records of an integer composition. St000770The major index of an integer partition when read from bottom to top. St000933The number of multipartitions of sizes given by an integer partition. St000937The number of positive values of the symmetric group character corresponding to the partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000993The multiplicity of the largest part of an integer partition. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St000264The girth of a graph, which is not a tree. St000706The product of the factorials of the multiplicities of an integer partition. St000707The product of the factorials of the parts. St000806The semiperimeter of the associated bargraph. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St001545The second Elser number of a connected graph. St001568The smallest positive integer that does not appear twice in the partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St001128The exponens consonantiae of a partition. St000418The number of Dyck paths that are weakly below a Dyck path. St000444The length of the maximal rise of a Dyck path. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000681The Grundy value of Chomp on Ferrers diagrams. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001531Number of partial orders contained in the poset determined by the Dyck path. St001959The product of the heights of the peaks of a Dyck path. St000045The number of linear extensions of a binary tree. St000060The greater neighbor of the maximum. St000061The number of nodes on the left branch of a binary tree. St000082The number of elements smaller than a binary tree in Tamari order. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000326The position of the first one in a binary word after appending a 1 at the end. St000327The number of cover relations in a poset. St000385The number of vertices with out-degree 1 in a binary tree. St000393The number of strictly increasing runs in a binary word. St000402Half the size of the symmetry class of a permutation. St000411The tree factorial of a binary tree. St000412The number of binary trees with the same underlying unordered tree. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000438The position of the last up step in a Dyck path. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000504The cardinality of the first block of a set partition. St000524The number of posets with the same order polynomial. St000525The number of posets with the same zeta polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000529The number of permutations whose descent word is the given binary word. St000530The number of permutations with the same descent word as the given permutation. St000543The size of the conjugacy class of a binary word. St000568The hook number of a binary tree. St000569The sum of the heights of the vertices of a binary tree. St000619The number of cyclic descents of a permutation. St000625The sum of the minimal distances to a greater element. St000626The minimal period of a binary word. St000630The length of the shortest palindromic decomposition of a binary word. St000633The size of the automorphism group of a poset. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000654The first descent of a permutation. St000680The Grundy value for Hackendot on posets. St000690The size of the conjugacy class of a permutation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000702The number of weak deficiencies of a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000729The minimal arc length of a set partition. St000744The length of the path to the largest entry in a standard Young tableau. St000817The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions. St000818The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions. St000823The number of unsplittable factors of the set partition. St000827The decimal representation of a binary word with a leading 1. St000844The size of the largest block in the direct sum decomposition of a permutation. St000876The number of factors in the Catalan decomposition of a binary word. St000885The number of critical steps in the Catalan decomposition of a binary word. St000886The number of permutations with the same antidiagonal sums. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000890The number of nonzero entries in an alternating sign matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000925The number of topologically connected components of a set partition. St000983The length of the longest alternating subword. St000988The orbit size of a permutation under Foata's bijection. St000990The first ascent of a permutation. St001062The maximal size of a block of a set partition. St001074The number of inversions of the cyclic embedding of a permutation. St001075The minimal size of a block of a set partition. St001081The number of minimal length factorizations of a permutation into star transpositions. St001246The maximal difference between two consecutive entries of a permutation. St001267The length of the Lyndon factorization of the binary word. St001313The number of Dyck paths above the lattice path given by a binary word. St001346The number of parking functions that give the same permutation. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001404The number of distinct entries in a Gelfand Tsetlin pattern. St001437The flex of a binary word. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001560The product of the cardinalities of the lower order ideal and upper order ideal generated by a permutation in weak order. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001637The number of (upper) dissectors of a poset. St001838The number of nonempty primitive factors of a binary word. St001915The size of the component corresponding to a necklace in Bulgarian solitaire.