Your data matches 435 different statistics following compositions of up to 3 maps.
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Matching statistic: St000070
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Mapping
Mp00065: Permutations —permutation poset⟶ Posets
St000070: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
 => 2
[1,2] => ([(0,1)],2)
 => 3
[2,1] => ([],2)
 => 4
Description
The number of antichains in a poset. An antichain in a poset $P$ is a subset of elements of $P$ which are pairwise incomparable. An order ideal is a subset $I$ of $P$ such that $a\in I$ and $b \leq_P a$ implies $b \in I$. Since there is a one-to-one correspondence between antichains and order ideals, this statistic is also the number of order ideals in a poset.
Matching statistic: St000104
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Mapping
Mp00065: Permutations —permutation poset⟶ Posets
St000104: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
 => 2
[1,2] => ([(0,1)],2)
 => 3
[2,1] => ([],2)
 => 4
Description
The number of facets in the order polytope of this poset.
Matching statistic: St000151
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Mapping
Mp00065: Permutations —permutation poset⟶ Posets
St000151: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
 => 2
[1,2] => ([(0,1)],2)
 => 3
[2,1] => ([],2)
 => 4
Description
The number of facets in the chain polytope of the poset.
Matching statistic: St000180
Mapping
Mp00065: Permutations —permutation poset⟶ Posets
St000180: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
 => 2
[1,2] => ([(0,1)],2)
 => 4
[2,1] => ([],2)
 => 3
Description
The number of chains of a poset.
Matching statistic: St000300
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Mapping
Mp00160: Permutations —graph of inversions⟶ Graphs
St000300: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
 => 2
[1,2] => ([],2)
 => 4
[2,1] => ([(0,1)],2)
 => 3
Description
The number of independent sets of vertices of a graph. An independent set of vertices of a graph $G$ is a subset $U \subset V(G)$ such that no two vertices in $U$ are adjacent. This is also the number of vertex covers of $G$ as the map $U \mapsto V(G)\setminus U$ is a bijection between independent sets of vertices and vertex covers. The size of the largest independent set, also called independence number of $G$, is [[St000093]]
Matching statistic: St000301
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Mapping
Mp00160: Permutations —graph of inversions⟶ Graphs
St000301: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
 => 2
[1,2] => ([],2)
 => 4
[2,1] => ([(0,1)],2)
 => 3
Description
The number of facets of the stable set polytope of a graph. The stable set polytope of a graph $G$ is the convex hull of the characteristic vectors of stable (or independent) sets of vertices of $G$ inside $\mathbb{R}^{V(G)}$.
Matching statistic: St001213
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Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001213: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1,0]
 => 2
[1,2] => [1,0,1,0]
 => 4
[2,1] => [1,1,0,0]
 => 3
Description
The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module.
Matching statistic: St001259
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Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001259: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1,0]
 => 2
[1,2] => [1,0,1,0]
 => 4
[2,1] => [1,1,0,0]
 => 3
Description
The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra.
Matching statistic: St001834
Mapping
Mp00160: Permutations —graph of inversions⟶ Graphs
St001834: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
 => 2
[1,2] => ([],2)
 => 3
[2,1] => ([(0,1)],2)
 => 4
Description
The number of non-isomorphic minors of a graph. A minor of a graph $G$ is a graph obtained from $G$ by repeatedly deleting or contracting edges, or removing isolated vertices. This statistic records the total number of (non-empty) non-isomorphic minors of a graph.
Matching statistic: St000231
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Mapping
Mp00151: Permutations —to cycle type⟶ Set partitions
St000231: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => {{1}}
 => 1 = 2 - 1
[1,2] => {{1},{2}}
 => 3 = 4 - 1
[2,1] => {{1,2}}
 => 2 = 3 - 1
Description
Sum of the maximal elements of the blocks of a set partition.
The following 425 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
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. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. 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. St001242The toal dimension of certain Sn modules determined by LLT polynomials associated with a Dyck path. St001243The sum of coefficients in the Schur basis of certain LLT polynomials associated with a Dyck path. 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. St001441The number of non-empty connected induced subgraphs of a graph. St001815The number of order preserving surjections from a poset to a total order. St000793The length of the longest partition in the vacillating tableau corresponding to a set partition. St001391The disjunction number of a graph. St000086The number of subgraphs. St000087The number of induced subgraphs. St000228The size of a partition. St000294The number of distinct factors of a binary word. St000393The number of strictly increasing runs in a binary word. St000395The sum of the heights of the peaks of a Dyck path. St000438The position of the last up step in a Dyck path. St000468The Hosoya index of a graph. St000518The number of distinct subsequences in a binary word. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000625The sum of the minimal distances to a greater element. St000708The product of the parts of an integer partition. St000815The number of semistandard Young tableaux of partition weight of given shape. St000915The Ore degree of a graph. St000926The clique-coclique number of a graph. St000933The number of multipartitions of sizes given by an integer partition. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001034The area of the parallelogram polyomino associated with the Dyck path. St001267The length of the Lyndon factorization of the binary word. St001279The sum of the parts of an integer partition that are at least two. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001379The number of inversions plus the major index of a permutation. 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. St001527The cyclic permutation representation number of an integer partition. St001616The number of neutral elements in a lattice. St001645The pebbling number of a connected graph. St001808The box weight or horizontal decoration of a Dyck path. St001855The number of signed permutations less than or equal to a signed permutation in left weak order. St001959The product of the heights of the peaks of a Dyck path. St000012The area of a Dyck path. St000081The number of edges of a graph. St000182The number of permutations whose cycle type is the given integer partition. St000224The sorting index of a permutation. St000271The chromatic index of a graph. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000289The decimal representation of a binary word. St000400The path length of an ordered tree. St000507The number of ascents of a standard tableau. St000519The largest length of a factor maximising the subword complexity. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000734The last entry in the first row of a standard tableau. St000795The mad of a permutation. St000841The largest opener of a perfect matching. St000922The minimal number such that all substrings of this length are unique. St000939The number of characters of the symmetric group whose value on the partition is positive. St000984The number of boxes below precisely one peak. St001111The weak 2-dynamic chromatic number of a graph. St001112The 3-weak dynamic number of a graph. St001117The game chromatic index of a graph. St001118The acyclic chromatic index of a graph. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001345The Hamming dimension of a graph. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001428The number of B-inversions of a signed permutation. St001619The number of non-isomorphic sublattices of a lattice. St001649The length of a longest trail in a graph. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001671Haglund's hag of a permutation. St001770The number of facets of a certain subword complex associated with the signed permutation. St001821The sorting index of a signed permutation. St001823The Stasinski-Voll length of a signed permutation. St001827The number of two-component spanning forests of a graph. St001894The depth of a signed permutation. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St000008The major index of the composition. St000137The Grundy value of an integer partition. St000304The load of a permutation. St000340The number of non-final maximal constant sub-paths of length greater than one. St000472The sum of the ascent bottoms of a permutation. St000811The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to Schur symmetric functions. St000961The shifted major index of a permutation. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001424The number of distinct squares in a binary word. St001613The binary logarithm of the size of the center of a lattice. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001621The number of atoms of a lattice. St001622The number of join-irreducible elements of a lattice. St001623The number of doubly irreducible elements of a lattice. St001625The Möbius invariant of a lattice. St000027The major index of a Dyck path. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000050The depth or height of a binary tree. St000064The number of one-box pattern of a permutation. St000189The number of elements in the poset. St000197The number of entries equal to positive one in the alternating sign matrix. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000325The width of the tree associated to a permutation. St000391The sum of the positions of the ones in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000470The number of runs in a permutation. St000626The minimal period of a binary word. St000631The number of distinct palindromic decompositions of a binary word. St000656The number of cuts of a poset. St000794The mak of a permutation. St000796The stat' of a permutation. 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. St000825The sum of the major and the inverse major index of a permutation. St000827The decimal representation of a binary word with a leading 1. St000863The length of the first row of the shifted shape of a permutation. St000876The number of factors in the Catalan decomposition of a binary word. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. 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 $c_{n-1}$. St000979Half of MacMahon's equal index of a Dyck path. St000981The length of the longest zigzag subpath. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001180Number of indecomposable injective modules with projective dimension at most 1. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. 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. St001437The flex of a binary word. St001462The number of factors of a standard tableaux under concatenation. St001486The number of corners of the ribbon associated with an integer composition. 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. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001554The number of distinct nonempty subtrees of a binary tree. St001614The cyclic permutation representation number of a skew partition. St001717The largest size of an interval in a poset. St001721The degree of a binary word. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St001809The index of the step at the first peak of maximal height in a Dyck path. St001817The number of flag weak exceedances of a signed permutation. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. 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. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000020The rank of the permutation. St000021The number of descents of a permutation. St000026The position of the first return of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000041The number of nestings of a perfect matching. St000047The number of standard immaculate tableaux of a given shape. St000054The first entry of the permutation. St000057The Shynar inversion number of a standard tableau. St000058The order of a permutation. St000060The greater neighbor of the maximum. St000067The inversion number of the alternating sign matrix. St000076The rank of the alternating sign matrix in the alternating sign matrix poset. St000077The number of boxed and circled entries. St000110The number of permutations less than or equal to a permutation in left weak order. St000133The "bounce" of a permutation. St000156The Denert index of a permutation. St000161The sum of the sizes of the right subtrees of a binary tree. St000185The weighted size of a partition. St000209Maximum difference of elements in cycles. St000210Minimum over maximum difference of elements in cycles. St000214The number of adjacencies of a permutation. St000216The absolute length of a permutation. St000238The number of indices that are not small weak excedances. St000240The number of indices that are not small excedances. St000246The number of non-inversions of a permutation. St000288The number of ones in a binary word. St000290The major index of a binary word. St000293The number of inversions of a binary word. St000295The length of the border of a binary word. St000305The inverse major index of a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000326The position of the first one in a binary word after appending a 1 at the end. 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. St000354The number of recoils of a permutation. St000398The sum of the depths of the vertices (or total internal path length) of a binary tree. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000420The number of Dyck paths that are weakly above a Dyck path. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000446The disorder of a permutation. St000451The length of the longest pattern of the form k 1 2. St000485The length of the longest cycle 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. St000501The size of the first part in the decomposition of a permutation. St000505The biggest entry in the block containing the 1. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000520The number of patterns in a permutation. St000539The number of odd inversions of a permutation. St000579The number of occurrences of the pattern {{1},{2}} such that 2 is a maximal element. St000617The number of global maxima of a Dyck path. St000619The number of cyclic descents of a permutation. St000638The number of up-down runs of a permutation. St000651The maximal size of a rise in a permutation. St000652The maximal difference between successive positions of a permutation. St000653The last descent of a permutation. St000670The reversal length of a permutation. St000675The number of centered multitunnels of a Dyck path. St000676The number of odd rises of a Dyck path. St000677The standardized bi-alternating inversion number of a permutation. St000678The number of up steps after the last double rise of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000690The size of the conjugacy class of a permutation. St000691The number of changes of a binary word. St000738The first entry in the last row of a standard tableau. St000740The last entry of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000744The length of the path to the largest entry in a standard Young tableau. St000792The Grundy value for the game of ruler on a binary word. St000797The stat`` of a permutation. St000798The makl of a permutation. St000806The semiperimeter of the associated bargraph. St000809The reduced reflection length of the permutation. St000816The number of standard composition tableaux of the composition. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St000833The comajor index of a permutation. St000839The largest opener of a set partition. St000844The size of the largest block in the direct sum decomposition of a permutation. St000847The number of standard Young tableaux whose descent set is the binary word. St000868The aid statistic in the sense of Shareshian-Wachs. St000874The position of the last double rise in a Dyck path. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000891The number of distinct diagonal sums of a permutation matrix. St000946The sum of the skew hook positions in a Dyck path. St000947The major index east count of a Dyck path. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St000957The number of Bruhat lower covers of a permutation. St000971The smallest closer of a set partition. St000983The length of the longest alternating subword. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001030Half the number of non-boundary horizontal edges in the fully packed loop corresponding to the alternating sign matrix. 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. St001052The length of the exterior of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001079The minimal length of a factorization of a permutation using the permutations (12)(34). St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001090The number of pop-stack-sorts needed to sort a permutation. St001096The size of the overlap set of a permutation. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001161The major index north count of a Dyck path. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. 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: St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001220The width of a permutation. 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. 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. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001246The maximal difference between two consecutive entries of a permutation. St001285The number of primes in the column sums of the two line notation of a permutation. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001313The number of Dyck paths above the lattice path given by a binary word. St001372The length of a longest cyclic run of ones of a binary word. St001375The pancake length of a permutation. St001376The Colless index of a binary tree. St001405The number of bonds in a permutation. St001433The flag major index of a signed permutation. St001439The number of even weak deficiencies and of odd weak exceedences. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001485The modular major index of a binary word. St001489The maximum of the number of descents and the number of inverse descents. St001497The position of the largest weak excedence of a permutation. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001528The number of permutations such that the product with the permutation has the same number of fixed points. St001530The depth of a Dyck path. 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. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001664The number of non-isomorphic subposets of a poset. St001726The number of visible inversions of a permutation. St001733The number of weak left to right maxima of a Dyck path. St001759The Rajchgot index of a permutation. St001760The number of prefix or suffix reversals needed to sort a permutation. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001806The upper middle entry of a permutation. St001807The lower middle entry of a permutation. St001819The flag Denert index of a signed permutation. St001838The number of nonempty primitive factors of a binary word. St001865The number of alignments of a signed permutation. St001874Lusztig's a-function for the symmetric group. St001892The flag excedance statistic of a signed permutation. St001893The flag descent of a signed permutation. St001930The weak major index of a binary word. St001955The number of natural descents for set-valued two row standard Young tableaux. St001956The comajor index for set-valued two-row standard Young tableaux. St001961The sum of the greatest common divisors of all pairs of parts. St000009The charge of a standard tableau. St000039The number of crossings of a permutation. St000053The number of valleys of the Dyck path. St000074The number of special entries. St000112The sum of the entries reduced by the index of their row in a semistandard tableau. St000120The number of left tunnels of a Dyck path. St000141The maximum drop size of a permutation. St000154The sum of the descent bottoms of a permutation. St000157The number of descents of a standard tableau. St000204The number of internal nodes of a binary tree. St000217The number of occurrences of the pattern 312 in a permutation. St000222The number of alignments in the permutation. St000253The crossing number of a set partition. St000306The bounce count of a Dyck path. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000331The number of upper interactions of a Dyck path. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000359The number of occurrences of the pattern 23-1. St000374The number of exclusive right-to-left minima of a permutation. St000389The number of runs of ones of odd length in a binary word. St000392The length of the longest run of ones in a binary word. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000427The number of occurrences of the pattern 123 or of the pattern 231 in a permutation. St000429The number of occurrences of the pattern 123 or of the pattern 321 in a permutation. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000461The rix statistic of a permutation. St000463The number of admissible inversions of a permutation. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000484The sum of St000483 over all subsequences of length at least three. St000490The intertwining number of a set partition. St000492The rob statistic of a set partition. St000499The rcb statistic of a set partition. St000503The maximal difference between two elements in a common block. St000554The number of occurrences of the pattern {{1,2},{3}} in a set partition. St000556The number of occurrences of the pattern {{1},{2,3}} in a set partition. St000574The number of occurrences of the pattern {{1},{2}} such that 1 is a minimal and 2 a maximal element. St000577The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element. St000586The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal. St000597The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, (2,3) are consecutive in a block. St000599The number of occurrences of the pattern {{1},{2,3}} such that (2,3) are consecutive in a block. St000605The number of occurrences of the pattern {{1},{2,3}} such that 3 is maximal, (2,3) are consecutive in a block. St000607The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 3 is maximal, (2,3) are consecutive in a block. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000646The number of big ascents of a permutation. St000648The number of 2-excedences of a permutation. St000663The number of right floats of a permutation. St000682The Grundy value of Welter's game on a binary word. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000692Babson and Steingrímsson's statistic of a permutation. St000703The number of deficiencies of a permutation. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000730The maximal arc length of a set partition. St000747A variant of the major index of a set partition. St000753The Grundy value for the game of Kayles on a binary word. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000881The number of short braid edges in the graph of braid moves of a permutation. St000921The number of internal inversions of a binary word. St000932The number of occurrences of the pattern UDU in a Dyck path. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St000956The maximal displacement of a permutation. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001160The number of proper blocks (or intervals) of a permutations. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. 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 $A$. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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 $eA$. St001209The pmaj statistic of a parking function. 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. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001273The projective dimension of the first term in an injective coresolution of the regular module. 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. 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. St001298The number of repeated entries in the Lehmer code of a permutation. St001402The number of separators in a permutation. St001413Half the length of the longest even length palindromic prefix of a binary word. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001427The number of descents of a signed permutation. St001429The number of negative entries in a signed permutation. St001430The number of positive entries in a signed permutation. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001480The number of simple summands of the module J^2/J^3. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001524The degree of symmetry of a binary word. St001535The number of cyclic alignments of a permutation. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001684The reduced word complexity of a permutation. St001769The reflection length of a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001870The number of positive entries followed by a negative entry in a signed permutation. St001895The oddness of a signed permutation. St001896The number of right descents of a signed permutations. St001931The weak major index of an integer composition regarded as a word. St001960The number of descents of a permutation minus one if its first entry is not one. St001965The number of decreasable positions in the corner sum matrix of an alternating sign matrix. St000187The determinant of an alternating sign matrix. St000878The number of ones minus the number of zeros of a binary word.