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Your data matches 503 different statistics following compositions of up to 3 maps.
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Matching statistic: St000142
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
St000142: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 0
[2]
=> 1
[1,1]
=> 0
[2,1]
=> 1
[1,1,1]
=> 0
[2,2]
=> 2
[2,1,1]
=> 1
[1,1,1,1]
=> 0
[2,2,1]
=> 2
[2,1,1,1]
=> 1
[1,1,1,1,1]
=> 0
[2,2,2]
=> 3
[2,2,1,1]
=> 2
[2,1,1,1,1]
=> 1
[1,1,1,1,1,1]
=> 0
[2,2,2,1]
=> 3
[2,2,1,1,1]
=> 2
[2,1,1,1,1,1]
=> 1
[1,1,1,1,1,1,1]
=> 0
[2,2,2,2]
=> 4
[2,2,2,1,1]
=> 3
[2,2,1,1,1,1]
=> 2
[2,2,2,2,1]
=> 4
[2,2,2,1,1,1]
=> 3
[2,2,2,2,2]
=> 5
[2,2,2,2,1,1]
=> 4
[2,2,2,2,2,1]
=> 5
[2,2,2,2,2,2]
=> 6
Description
The number of even parts of a partition.
Matching statistic: St001251
St001251: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 0
[2]
=> 1
[1,1]
=> 0
[2,1]
=> 1
[1,1,1]
=> 0
[2,2]
=> 2
[2,1,1]
=> 1
[1,1,1,1]
=> 0
[2,2,1]
=> 2
[2,1,1,1]
=> 1
[1,1,1,1,1]
=> 0
[2,2,2]
=> 3
[2,2,1,1]
=> 2
[2,1,1,1,1]
=> 1
[1,1,1,1,1,1]
=> 0
[2,2,2,1]
=> 3
[2,2,1,1,1]
=> 2
[2,1,1,1,1,1]
=> 1
[1,1,1,1,1,1,1]
=> 0
[2,2,2,2]
=> 4
[2,2,2,1,1]
=> 3
[2,2,1,1,1,1]
=> 2
[2,2,2,2,1]
=> 4
[2,2,2,1,1,1]
=> 3
[2,2,2,2,2]
=> 5
[2,2,2,2,1,1]
=> 4
[2,2,2,2,2,1]
=> 5
[2,2,2,2,2,2]
=> 6
Description
The number of parts of a partition that are not congruent 1 modulo 3.
Matching statistic: St001252
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
St001252: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 0
[2]
=> 1
[1,1]
=> 0
[2,1]
=> 1
[1,1,1]
=> 0
[2,2]
=> 2
[2,1,1]
=> 1
[1,1,1,1]
=> 0
[2,2,1]
=> 2
[2,1,1,1]
=> 1
[1,1,1,1,1]
=> 0
[2,2,2]
=> 3
[2,2,1,1]
=> 2
[2,1,1,1,1]
=> 1
[1,1,1,1,1,1]
=> 0
[2,2,2,1]
=> 3
[2,2,1,1,1]
=> 2
[2,1,1,1,1,1]
=> 1
[1,1,1,1,1,1,1]
=> 0
[2,2,2,2]
=> 4
[2,2,2,1,1]
=> 3
[2,2,1,1,1,1]
=> 2
[2,2,2,2,1]
=> 4
[2,2,2,1,1,1]
=> 3
[2,2,2,2,2]
=> 5
[2,2,2,2,1,1]
=> 4
[2,2,2,2,2,1]
=> 5
[2,2,2,2,2,2]
=> 6
Description
Half the sum of the even parts of a partition.
Matching statistic: St001280
St001280: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 0
[2]
=> 1
[1,1]
=> 0
[2,1]
=> 1
[1,1,1]
=> 0
[2,2]
=> 2
[2,1,1]
=> 1
[1,1,1,1]
=> 0
[2,2,1]
=> 2
[2,1,1,1]
=> 1
[1,1,1,1,1]
=> 0
[2,2,2]
=> 3
[2,2,1,1]
=> 2
[2,1,1,1,1]
=> 1
[1,1,1,1,1,1]
=> 0
[2,2,2,1]
=> 3
[2,2,1,1,1]
=> 2
[2,1,1,1,1,1]
=> 1
[1,1,1,1,1,1,1]
=> 0
[2,2,2,2]
=> 4
[2,2,2,1,1]
=> 3
[2,2,1,1,1,1]
=> 2
[2,2,2,2,1]
=> 4
[2,2,2,1,1,1]
=> 3
[2,2,2,2,2]
=> 5
[2,2,2,2,1,1]
=> 4
[2,2,2,2,2,1]
=> 5
[2,2,2,2,2,2]
=> 6
Description
The number of parts of an integer partition that are at least two.
Matching statistic: St001657
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
St001657: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 0
[2]
=> 1
[1,1]
=> 0
[2,1]
=> 1
[1,1,1]
=> 0
[2,2]
=> 2
[2,1,1]
=> 1
[1,1,1,1]
=> 0
[2,2,1]
=> 2
[2,1,1,1]
=> 1
[1,1,1,1,1]
=> 0
[2,2,2]
=> 3
[2,2,1,1]
=> 2
[2,1,1,1,1]
=> 1
[1,1,1,1,1,1]
=> 0
[2,2,2,1]
=> 3
[2,2,1,1,1]
=> 2
[2,1,1,1,1,1]
=> 1
[1,1,1,1,1,1,1]
=> 0
[2,2,2,2]
=> 4
[2,2,2,1,1]
=> 3
[2,2,1,1,1,1]
=> 2
[2,2,2,2,1]
=> 4
[2,2,2,1,1,1]
=> 3
[2,2,2,2,2]
=> 5
[2,2,2,2,1,1]
=> 4
[2,2,2,2,2,1]
=> 5
[2,2,2,2,2,2]
=> 6
Description
The number of twos in an integer partition.
The total number of twos in all partitions of $n$ is equal to the total number of singletons [[St001484]] in all partitions of $n-1$, see [1].
Matching statistic: St000345
St000345: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 1 = 0 + 1
[2]
=> 2 = 1 + 1
[1,1]
=> 1 = 0 + 1
[2,1]
=> 2 = 1 + 1
[1,1,1]
=> 1 = 0 + 1
[2,2]
=> 3 = 2 + 1
[2,1,1]
=> 2 = 1 + 1
[1,1,1,1]
=> 1 = 0 + 1
[2,2,1]
=> 3 = 2 + 1
[2,1,1,1]
=> 2 = 1 + 1
[1,1,1,1,1]
=> 1 = 0 + 1
[2,2,2]
=> 4 = 3 + 1
[2,2,1,1]
=> 3 = 2 + 1
[2,1,1,1,1]
=> 2 = 1 + 1
[1,1,1,1,1,1]
=> 1 = 0 + 1
[2,2,2,1]
=> 4 = 3 + 1
[2,2,1,1,1]
=> 3 = 2 + 1
[2,1,1,1,1,1]
=> 2 = 1 + 1
[1,1,1,1,1,1,1]
=> 1 = 0 + 1
[2,2,2,2]
=> 5 = 4 + 1
[2,2,2,1,1]
=> 4 = 3 + 1
[2,2,1,1,1,1]
=> 3 = 2 + 1
[2,2,2,2,1]
=> 5 = 4 + 1
[2,2,2,1,1,1]
=> 4 = 3 + 1
[2,2,2,2,2]
=> 6 = 5 + 1
[2,2,2,2,1,1]
=> 5 = 4 + 1
[2,2,2,2,2,1]
=> 6 = 5 + 1
[2,2,2,2,2,2]
=> 7 = 6 + 1
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: St000935
St000935: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 1 = 0 + 1
[2]
=> 2 = 1 + 1
[1,1]
=> 1 = 0 + 1
[2,1]
=> 2 = 1 + 1
[1,1,1]
=> 1 = 0 + 1
[2,2]
=> 3 = 2 + 1
[2,1,1]
=> 2 = 1 + 1
[1,1,1,1]
=> 1 = 0 + 1
[2,2,1]
=> 3 = 2 + 1
[2,1,1,1]
=> 2 = 1 + 1
[1,1,1,1,1]
=> 1 = 0 + 1
[2,2,2]
=> 4 = 3 + 1
[2,2,1,1]
=> 3 = 2 + 1
[2,1,1,1,1]
=> 2 = 1 + 1
[1,1,1,1,1,1]
=> 1 = 0 + 1
[2,2,2,1]
=> 4 = 3 + 1
[2,2,1,1,1]
=> 3 = 2 + 1
[2,1,1,1,1,1]
=> 2 = 1 + 1
[1,1,1,1,1,1,1]
=> 1 = 0 + 1
[2,2,2,2]
=> 5 = 4 + 1
[2,2,2,1,1]
=> 4 = 3 + 1
[2,2,1,1,1,1]
=> 3 = 2 + 1
[2,2,2,2,1]
=> 5 = 4 + 1
[2,2,2,1,1,1]
=> 4 = 3 + 1
[2,2,2,2,2]
=> 6 = 5 + 1
[2,2,2,2,1,1]
=> 5 = 4 + 1
[2,2,2,2,2,1]
=> 6 = 5 + 1
[2,2,2,2,2,2]
=> 7 = 6 + 1
Description
The number of ordered refinements of an integer partition.
This is, for an integer partition $\mu = (\mu_1,\ldots,\mu_n)$ the number of integer partition $\lambda = (\lambda_1,\ldots,\lambda_m)$ such that there are indices $1 = a_0 < \ldots < a_n = m$ with $\mu_j = \lambda_{a_{j-1}} + \ldots + \lambda_{a_j-1}$.
Matching statistic: St001389
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
St001389: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> 1 = 0 + 1
[2]
=> 2 = 1 + 1
[1,1]
=> 1 = 0 + 1
[2,1]
=> 2 = 1 + 1
[1,1,1]
=> 1 = 0 + 1
[2,2]
=> 3 = 2 + 1
[2,1,1]
=> 2 = 1 + 1
[1,1,1,1]
=> 1 = 0 + 1
[2,2,1]
=> 3 = 2 + 1
[2,1,1,1]
=> 2 = 1 + 1
[1,1,1,1,1]
=> 1 = 0 + 1
[2,2,2]
=> 4 = 3 + 1
[2,2,1,1]
=> 3 = 2 + 1
[2,1,1,1,1]
=> 2 = 1 + 1
[1,1,1,1,1,1]
=> 1 = 0 + 1
[2,2,2,1]
=> 4 = 3 + 1
[2,2,1,1,1]
=> 3 = 2 + 1
[2,1,1,1,1,1]
=> 2 = 1 + 1
[1,1,1,1,1,1,1]
=> 1 = 0 + 1
[2,2,2,2]
=> 5 = 4 + 1
[2,2,2,1,1]
=> 4 = 3 + 1
[2,2,1,1,1,1]
=> 3 = 2 + 1
[2,2,2,2,1]
=> 5 = 4 + 1
[2,2,2,1,1,1]
=> 4 = 3 + 1
[2,2,2,2,2]
=> 6 = 5 + 1
[2,2,2,2,1,1]
=> 5 = 4 + 1
[2,2,2,2,2,1]
=> 6 = 5 + 1
[2,2,2,2,2,2]
=> 7 = 6 + 1
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: St000149
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
St000149: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000149: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> [1]
=> 0
[2]
=> [2]
=> 1
[1,1]
=> [1,1]
=> 0
[2,1]
=> [3]
=> 1
[1,1,1]
=> [1,1,1]
=> 0
[2,2]
=> [4]
=> 2
[2,1,1]
=> [3,1]
=> 1
[1,1,1,1]
=> [1,1,1,1]
=> 0
[2,2,1]
=> [5]
=> 2
[2,1,1,1]
=> [3,1,1]
=> 1
[1,1,1,1,1]
=> [1,1,1,1,1]
=> 0
[2,2,2]
=> [6]
=> 3
[2,2,1,1]
=> [5,1]
=> 2
[2,1,1,1,1]
=> [3,1,1,1]
=> 1
[1,1,1,1,1,1]
=> [1,1,1,1,1,1]
=> 0
[2,2,2,1]
=> [7]
=> 3
[2,2,1,1,1]
=> [5,1,1]
=> 2
[2,1,1,1,1,1]
=> [3,1,1,1,1]
=> 1
[1,1,1,1,1,1,1]
=> [1,1,1,1,1,1,1]
=> 0
[2,2,2,2]
=> [8]
=> 4
[2,2,2,1,1]
=> [7,1]
=> 3
[2,2,1,1,1,1]
=> [5,1,1,1]
=> 2
[2,2,2,2,1]
=> [9]
=> 4
[2,2,2,1,1,1]
=> [7,1,1]
=> 3
[2,2,2,2,2]
=> [10]
=> 5
[2,2,2,2,1,1]
=> [9,1]
=> 4
[2,2,2,2,2,1]
=> [11]
=> 5
[2,2,2,2,2,2]
=> [12]
=> 6
Description
The number of cells of the partition whose leg is zero and arm is odd.
This statistic is equidistributed with [[St000143]], see [1].
Matching statistic: St000150
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
St000150: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000150: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
=> [1]
=> 0
[2]
=> [1,1]
=> 1
[1,1]
=> [2]
=> 0
[2,1]
=> [1,1,1]
=> 1
[1,1,1]
=> [2,1]
=> 0
[2,2]
=> [1,1,1,1]
=> 2
[2,1,1]
=> [2,1,1]
=> 1
[1,1,1,1]
=> [4]
=> 0
[2,2,1]
=> [1,1,1,1,1]
=> 2
[2,1,1,1]
=> [2,1,1,1]
=> 1
[1,1,1,1,1]
=> [4,1]
=> 0
[2,2,2]
=> [1,1,1,1,1,1]
=> 3
[2,2,1,1]
=> [2,1,1,1,1]
=> 2
[2,1,1,1,1]
=> [4,1,1]
=> 1
[1,1,1,1,1,1]
=> [4,2]
=> 0
[2,2,2,1]
=> [1,1,1,1,1,1,1]
=> 3
[2,2,1,1,1]
=> [2,1,1,1,1,1]
=> 2
[2,1,1,1,1,1]
=> [4,1,1,1]
=> 1
[1,1,1,1,1,1,1]
=> [4,2,1]
=> 0
[2,2,2,2]
=> [1,1,1,1,1,1,1,1]
=> 4
[2,2,2,1,1]
=> [2,1,1,1,1,1,1]
=> 3
[2,2,1,1,1,1]
=> [4,1,1,1,1]
=> 2
[2,2,2,2,1]
=> [1,1,1,1,1,1,1,1,1]
=> 4
[2,2,2,1,1,1]
=> [2,1,1,1,1,1,1,1]
=> 3
[2,2,2,2,2]
=> [1,1,1,1,1,1,1,1,1,1]
=> 5
[2,2,2,2,1,1]
=> [2,1,1,1,1,1,1,1,1]
=> 4
[2,2,2,2,2,1]
=> [1,1,1,1,1,1,1,1,1,1,1]
=> 5
[2,2,2,2,2,2]
=> [1,1,1,1,1,1,1,1,1,1,1,1]
=> 6
Description
The floored half-sum of the multiplicities of a partition.
This statistic is equidistributed with [[St000143]] and [[St000149]], see [1].
The following 493 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000185The weighted size of a partition. St000377The dinv defect of an integer partition. St000877The depth of the binary word interpreted as a path. St001176The size of a partition minus its first part. St000010The length of the partition. St000326The position of the first one in a binary word after appending a 1 at the end. St000814The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions. St000012The area of a Dyck path. St000147The largest part of an integer partition. St000148The number of odd parts of a partition. St000160The multiplicity of the smallest part of a partition. St000228The size of a partition. St000288The number of ones in a binary word. St000293The number of inversions of a binary word. St000297The number of leading ones in a binary word. St000369The dinv deficit of a Dyck path. St000384The maximal part of the shifted composition of an integer partition. St000391The sum of the positions of the ones in a binary word. St000392The length of the longest run of ones in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000459The hook length of the base cell of a partition. St000475The number of parts equal to 1 in a partition. St000519The largest length of a factor maximising the subword complexity. St000548The number of different non-empty partial sums of an integer partition. St000784The maximum of the length and the largest part of the integer partition. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000867The sum of the hook lengths in the first row of an integer partition. St000992The alternating sum of the parts of an integer partition. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001127The sum of the squares of the parts of a partition. St001372The length of a longest cyclic run of ones of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001721The degree of a binary word. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000026The position of the first return of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000378The diagonal inversion number of an integer partition. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000532The total number of rook placements on a Ferrers board. St000808The number of up steps of the associated bargraph. 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. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001400The total number of Littlewood-Richardson tableaux of given shape. St001814The number of partitions interlacing the given partition. St000011The number of touch points (or returns) of a Dyck path. St000013The height of a Dyck path. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000025The number of initial rises of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000053The number of valleys of the Dyck path. St000237The number of small exceedances. St000290The major index of a binary word. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000376The bounce deficit of a Dyck path. St000433The number of occurrences of the pattern 132 or of the pattern 321 in a permutation. St000445The number of rises of length 1 of a Dyck path. St000507The number of ascents of a standard tableau. St000549The number of odd partial sums of an integer partition. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000676The number of odd rises of a Dyck path. St000682The Grundy value of Welter's game on a binary word. St000921The number of internal inversions of a binary word. St000996The number of exclusive left-to-right maxima of a permutation. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001034The area of the parallelogram polyomino associated with the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001090The number of pop-stack-sorts needed to sort a permutation. St001161The major index north count of a Dyck path. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001485The modular major index of a binary word. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001759The Rajchgot index of a permutation. St001777The number of weak descents in an integer composition. St001816Eigenvalues of the top-to-random operator acting on a simple module. St000058The order of a permutation. St000093The cardinality of a maximal independent set of vertices of a graph. St000110The number of permutations less than or equal to a permutation in left weak order. St000383The last part of an integer composition. St000505The biggest entry in the block containing the 1. St000668The least common multiple of the parts of the partition. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000708The product of the parts of an integer partition. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows:
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. St001733The number of weak left to right maxima of a Dyck path. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St000439The position of the first down step of a Dyck path. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000059The inversion number of a standard tableau as defined by Haglund and Stevens. St000157The number of descents of a standard tableau. St000169The cocharge of a standard tableau. St000330The (standard) major index of a standard tableau. St000336The leg major index of a standard tableau. St000648The number of 2-excedences of a permutation. St000984The number of boxes below precisely one peak. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St000738The first entry in the last row of a standard tableau. St000009The charge of a standard tableau. St000141The maximum drop size of a permutation. St000209Maximum difference of elements in cycles. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000352The Elizalde-Pak rank of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000503The maximal difference between two elements in a common block. St000534The number of 2-rises of a permutation. St000572The dimension exponent of a set partition. St000579The number of occurrences of the pattern {{1},{2}} such that 2 is a maximal element. St000662The staircase size of the code of a permutation. St000703The number of deficiencies of a permutation. St000728The dimension of a set partition. St000730The maximal arc length of a set partition. St000742The number of big ascents of a permutation after prepending zero. St000932The number of occurrences of the pattern UDU in a Dyck path. St000946The sum of the skew hook positions in a Dyck path. St000947The major index east count of a Dyck path. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000054The first entry of the permutation. St000420The number of Dyck paths that are weakly above a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000734The last entry in the first row of a standard tableau. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001808The box weight or horizontal decoration of a Dyck path. St000321The number of integer partitions of n that are dominated by an integer partition. St000074The number of special entries. St000245The number of ascents of a permutation. St000246The number of non-inversions of a permutation. St000441The number of successions of a permutation. St000665The number of rafts of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000834The number of right outer peaks of a permutation. St000733The row containing the largest entry of a standard tableau. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000204The number of internal nodes of a binary tree. St000291The number of descents of a binary word. St000389The number of runs of ones of odd length in a binary word. St000390The number of runs of ones in a binary word. St000539The number of odd inversions of a permutation. St000646The number of big ascents of a permutation. St000653The last descent of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St001726The number of visible inversions of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000306The bounce count of a Dyck path. St001424The number of distinct squares in a binary word. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St000008The major index of the composition. St000041The number of nestings of a perfect matching. St000651The maximal size of a rise in a permutation. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001246The maximal difference between two consecutive entries of a permutation. St001268The size of the largest ordinal summand in the poset. St000431The number of occurrences of the pattern 213 or of the pattern 321 in a permutation. St000693The modular (standard) major index of a standard tableau. St001697The shifted natural comajor index of a standard Young tableau. St000035The number of left outer peaks of a permutation. St000161The sum of the sizes of the right subtrees of a binary tree. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St000501The size of the first part in the decomposition of a permutation. St001462The number of factors of a standard tableaux under concatenation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000428The number of occurrences of the pattern 123 or of the pattern 213 in a permutation. St000460The hook length of the last cell along the main diagonal of an integer partition. St000667The greatest common divisor of the parts of the partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001360The number of covering relations in Young's lattice below a partition. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001527The cyclic permutation representation number of an integer partition. St001571The Cartan determinant of the integer partition. St001933The largest multiplicity of a part in an integer partition. St000145The Dyson rank of a partition. St000240The number of indices that are not small excedances. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St000004The major index of a permutation. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000015The number of peaks of a Dyck path. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000051The size of the left subtree of a binary tree. St000057The Shynar inversion number of a standard tableau. St000067The inversion number of the alternating sign matrix. St000076The rank of the alternating sign matrix in the alternating sign matrix poset. St000120The number of left tunnels of a Dyck path. St000144The pyramid weight of the Dyck path. St000154The sum of the descent bottoms of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000156The Denert index of a permutation. St000224The sorting index of a permutation. St000305The inverse major index of a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000331The number of upper interactions of a Dyck path. St000339The maf index of a permutation. St000395The sum of the heights of the peaks of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000531The leading coefficient of the rook polynomial of an integer partition. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000794The mak of a permutation. St000796The stat' of a permutation. St000809The reduced reflection length of the permutation. St000833The comajor index of a permutation. St000884The number of isolated descents of a permutation. St000922The minimal number such that all substrings of this length are unique. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000982The length of the longest constant subword. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001205The number of non-simple indecomposable projective-injective modules of the algebra $eAe$ in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. 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. St001228The vector space dimension of the space of module homomorphisms between J and itself when J denotes the Jacobson radical of the corresponding Nakayama algebra. St001254The vector space dimension of the first extension-group between A/soc(A) and J when A is the corresponding Nakayama algebra with Jacobson radical J. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001274The number of indecomposable injective modules with projective dimension equal to two. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001397Number of pairs of incomparable elements in a finite poset. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001498The normalised height of a Nakayama algebra with magnitude 1. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001523The degree of symmetry of a Dyck path. St001530The depth of a Dyck path. St001614The cyclic permutation representation number of a skew partition. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001660The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board. St001688The sum of the squares of the heights of the peaks of a Dyck path. St001809The index of the step at the first peak of maximal height in a Dyck path. St000393The number of strictly increasing runs in a binary word. St000442The maximal area to the right of an up step of a Dyck path. St000485The length of the longest cycle of a permutation. St000529The number of permutations whose descent word is the given binary word. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000740The last entry of a permutation. St000874The position of the last double rise in a Dyck path. St000883The number of longest increasing subsequences of a permutation. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St000968We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n−1}]$ by adding $c_0$ to $c_{n−1}$. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001267The length of the Lyndon factorization of the binary word. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001437The flex of a binary word. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001658The total number of rook placements on a Ferrers board. St001955The number of natural descents for set-valued two row standard Young tableaux. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001838The number of nonempty primitive factors of a binary word. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. St001480The number of simple summands of the module J^2/J^3. St000214The number of adjacencies of a permutation. St000216The absolute length of a permutation. St000335The difference of lower and upper interactions. St000443The number of long tunnels of a Dyck path. St000670The reversal length of a permutation. St000692Babson and Steingrímsson's statistic of a permutation. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001959The product of the heights of the peaks of a Dyck path. St000014The number of parking functions supported by a Dyck path. St000061The number of nodes on the left branch of a binary tree. St000082The number of elements smaller than a binary tree in Tamari order. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000839The largest opener of a set partition. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. St001180Number of indecomposable injective modules with projective dimension at most 1. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001346The number of parking functions that give the same permutation. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St000211The rank of the set partition. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000711The number of big exceedences of a permutation. St000423The number of occurrences of the pattern 123 or of the pattern 132 in a permutation. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000492The rob statistic of a set partition. St000493The los statistic of a set partition. St000498The lcs statistic of a set partition. St000499The rcb statistic of a set partition. St000710The number of big deficiencies of a permutation. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001412Number of minimal entries in the Bruhat order matrix of a permutation. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001489The maximum of the number of descents and the number of inverse descents. St001584The area statistic between a Dyck path and its bounce path. St001665The number of pure excedances of a permutation. St001729The number of visible descents of a permutation. St001737The number of descents of type 2 in a permutation. St001799The number of proper separations of a graph. St001801Half the number of preimage-image pairs of different parity in a permutation. St001928The number of non-overlapping descents in a permutation. St000060The greater neighbor of the maximum. St000105The number of blocks in the set partition. St000470The number of runs in a permutation. St000971The smallest closer of a set partition. St000251The number of nonsingleton blocks of a set partition. St000502The number of successions of a set partitions. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000354The number of recoils of a permutation. St000494The number of inversions of distance at most 3 of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000795The mad of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001061The number of indices that are both descents and recoils of a permutation. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St000504The cardinality of the first block of a set partition. St000678The number of up steps after the last double rise of a Dyck path. St000925The number of topologically connected components of a set partition. St001062The maximal size of a block of a set partition. St001298The number of repeated entries in the Lehmer code of a permutation. St000007The number of saliances of the permutation. St000446The disorder of a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St000654The first descent of a permutation. St000341The non-inversion sum of a permutation. St000477The weight of a partition according to Alladi. St000770The major index of an integer partition when read from bottom to top. St000993The multiplicity of the largest part of an integer partition. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St000681The Grundy value of Chomp on Ferrers diagrams. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000021The number of descents of a permutation. St000055The inversion sum of a permutation. St000133The "bounce" of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000238The number of indices that are not small weak excedances. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000674The number of hills of a Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001114The number of odd descents of a permutation. St001118The acyclic chromatic index of a graph. St001152The number of pairs with even minimum in a perfect matching. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001684The reduced word complexity of a permutation. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St001874Lusztig's a-function for the symmetric group. St000062The length of the longest increasing subsequence of the permutation. St000213The number of weak exceedances (also weak excedences) of a permutation. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000325The width of the tree associated to a permutation. St000567The sum of the products of all pairs of parts. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000744The length of the path to the largest entry in a standard Young tableau. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000991The number of right-to-left minima of a permutation. St001128The exponens consonantiae of a partition. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St000083The number of left oriented leafs of a binary tree except the first one. St001859The number of factors of the Stanley symmetric function associated with a permutation. St000702The number of weak deficiencies of a permutation. St000898The number of maximal entries in the last diagonal of the monotone triangle. St001557The number of inversions of the second entry of a permutation. St000806The semiperimeter of the associated bargraph. St000219The number of occurrences of the pattern 231 in a permutation. St001965The number of decreasable positions in the corner sum matrix of an alternating sign matrix. St000327The number of cover relations in a poset. St001569The maximal modular displacement of a permutation. St001668The number of points of the poset minus the width of the poset. St001948The number of augmented double ascents of a permutation. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St000136The dinv of a parking function. St000194The number of primary dinversion pairs of a labelled dyck path corresponding to a parking function. 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 $K[x]/(x^n)$. St001772The number of occurrences of the signed pattern 12 in a signed permutation. St001935The number of ascents in a parking function. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St000260The radius of a connected graph. St001060The distinguishing index of a graph. St001960The number of descents of a permutation minus one if its first entry is not one. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000023The number of inner peaks of a permutation. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000497The lcb statistic of a set partition. St001469The holeyness of a permutation. St001520The number of strict 3-descents. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St000075The orbit size of a standard tableau under promotion. St000099The number of valleys of a permutation, including the boundary. St000166The depth minus 1 of an ordered tree. St000455The second largest eigenvalue of a graph if it is integral. St000522The number of 1-protected nodes of a rooted tree. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000521The number of distinct subtrees of an ordered tree. St001811The Castelnuovo-Mumford regularity of a permutation. St000632The jump number of the poset. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001722The number of minimal chains with small intervals between a binary word and the top element. St000307The number of rowmotion orbits of a poset. St000717The number of ordinal summands of a poset.
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