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. 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. St001267The length of the Lyndon factorization of the 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. 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. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001190Number of simple modules with projective dimension at most 4 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 St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St000015The number of peaks of a Dyck path. St000019The cardinality of the support of a permutation. St000030The sum of the descent differences of a permutations. St000050The depth or height of a binary tree. St000062The length of the longest increasing subsequence of the permutation. St000134The size of the orbit of an alternating sign matrix under gyration. St000203The number of external nodes of a binary tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000239The number of small weak excedances. St000290The major index of a binary word. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000443The number of long tunnels of a Dyck path. St000528The height of a poset. St000672The number of minimal elements in Bruhat order not less than the permutation. St000676The number of odd rises of a Dyck path. St000696The number of cycles in the breakpoint graph of a permutation. St000808The number of up steps of the associated bargraph. St000863The length of the first row of the shifted shape of a permutation. St000912The number of maximal antichains in a poset. St000956The maximal displacement of a permutation. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. 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. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001090The number of pop-stack-sorts needed to sort a permutation. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001187The number of simple modules with grade at least one 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: St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001224Let X be the direct sum of all simple modules of 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. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. 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. St001343The dimension of the reduced incidence algebra of a poset. 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. St001485The modular major index of a binary word. St001554The number of distinct nonempty subtrees of a binary tree. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001925The minimal number of zeros in a row of an alternating sign matrix. St001929The number of meanders with top half given by the noncrossing matching corresponding to the Dyck path. St001958The degree of the polynomial interpolating the values of a permutation. St000018The number of inversions of a permutation. St000024The number of double up and double down steps of a Dyck path. St000029The depth of a permutation. St000053The number of valleys of the Dyck path. St000080The rank of the poset. St000197The number of entries equal to positive one in the alternating sign matrix. St000209Maximum difference of elements in cycles. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000245The number of ascents of a permutation. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000288The number of ones in a binary word. St000306The bounce count of a Dyck path. St000331The number of upper interactions of a Dyck path. St000336The leg major index of a standard tableau. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000445The number of rises of length 1 of a Dyck path. St000501The size of the first part in the decomposition of a permutation. St000744The length of the path to the largest entry in a standard Young tableau. St000809The reduced reflection length of the permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000876The number of factors in the Catalan decomposition of a binary word. St000890The number of nonzero entries in an alternating sign matrix. St000924The number of topologically connected components of a perfect matching. St000957The number of Bruhat lower covers of a permutation. St001004The number of indices that are either left-to-right maxima or right-to-left minima. 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. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001034The area of the parallelogram polyomino associated with the Dyck path. St001065Number of indecomposable reflexive 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. St001096The size of the overlap set of a permutation. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001142The projective dimension of the socle of the regular module as a bimodule 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. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. 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 $eA$. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001298The number of repeated entries in the Lehmer code of a permutation. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001405The number of bonds in a permutation. St001480The number of simple summands of the module J^2/J^3. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. 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. St000026The position of the first return of a Dyck path. St000044The number of vertices of the unicellular map given by a perfect matching. St000058The order of a permutation. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000673The number of non-fixed points of a permutation. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001012Number of simple modules with projective dimension at most 2 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. 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. St000806The semiperimeter of the associated bargraph. St001468The smallest fixpoint of a permutation. St000784The maximum of the length and the largest part of the integer partition. St000013The height of a Dyck path. St000293The number of inversions of a binary word. St000010The length of the partition. St000147The largest part of an integer partition. St000326The position of the first one in a binary word after appending a 1 at the end. St000668The least common multiple of the parts of the partition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000011The number of touch points (or returns) of a Dyck path. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000475The number of parts equal to 1 in a partition. St001176The size of a partition minus its first part. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000877The depth of the binary word interpreted as a path. St000297The number of leading ones in a binary word. St000392The length of the longest run of ones in a binary word. St000983The length of the longest alternating subword. St001372The length of a longest cyclic run of ones of a binary word. St000390The number of runs of ones in a binary word. St000691The number of changes of a binary word. St001415The length of the longest palindromic prefix of a binary word. St001437The flex of a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St000391The sum of the positions of the ones in a binary word. St000507The number of ascents of a standard tableau. St000753The Grundy value for the game of Kayles on a binary word. St001313The number of Dyck paths above the lattice path given by a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001721The degree of a binary word. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000682The Grundy value of Welter's game on a binary word. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St000941The number of characters of the symmetric group whose value on the partition is even. St000141The maximum drop size of a permutation. St000214The number of adjacencies of a permutation. St000662The staircase size of the code of a permutation. St000717The number of ordinal summands of a poset. St000906The length of the shortest maximal chain in a poset. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. 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 $eA$. St000054The first entry of the permutation. St000223The number of nestings in the permutation. St000366The number of double descents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000631The number of distinct palindromic decompositions of a binary word. St000643The size of the largest orbit of antichains under Panyushev complementation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000883The number of longest increasing subsequences of a permutation. St000922The minimal number such that all substrings of this length are unique. St001052The length of the exterior of a permutation. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001668The number of points of the poset minus the width of the poset. St001884The number of borders of a binary word. St000295The length of the border of a binary word. St000837The number of ascents of distance 2 of a permutation. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001524The degree of symmetry of a binary word. St000734The last entry in the first row of a standard tableau. St000738The first entry in the last row of a standard tableau. St000215The number of adjacencies of a permutation, zero appended. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000374The number of exclusive right-to-left minima of a permutation. St000703The number of deficiencies of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000159The number of distinct parts of the integer partition. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000820The number of compositions obtained by rotating the composition. St000783The side length of the largest staircase partition fitting into a partition. St000007The number of saliances of the permutation. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St000439The position of the first down step of a Dyck path. St000031The number of cycles in the cycle decomposition of a permutation. St000022The number of fixed points of a permutation. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000765The number of weak records in an integer composition. St000237The number of small exceedances. St001933The largest multiplicity of a part in an integer partition. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001961The sum of the greatest common divisors of all pairs of parts. St000451The length of the longest pattern of the form k 1 2. St000651The maximal size of a rise in a permutation. St000356The number of occurrences of the pattern 13-2. St000433The number of occurrences of the pattern 132 or of the pattern 321 in a permutation. St000463The number of admissible inversions of a permutation. St000670The reversal length of a permutation. St000167The number of leaves of an ordered tree. St000052The number of valleys of a Dyck path not on the x-axis. St000678The number of up steps after the last double rise of a Dyck path. St001462The number of factors of a standard tableaux under concatenation. St000359The number of occurrences of the pattern 23-1. St000442The maximal area to the right of an up step of a Dyck path. St000825The sum of the major and the inverse major index of a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001726The number of visible inversions of a permutation. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000925The number of topologically connected components of a set partition. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St000220The number of occurrences of the pattern 132 in a permutation. St000247The number of singleton blocks of a set partition. St000446The disorder of a permutation. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000831The number of indices that are either descents or recoils. St000975The length of the boundary minus the length of the trunk of an ordered tree. St001760The number of prefix or suffix reversals needed to sort a permutation. St000069The number of maximal elements of a poset. St000110The number of permutations less than or equal to a permutation in left weak order. St000153The number of adjacent cycles 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. St001432The order dimension of the partition. St000383The last part of an integer composition. St000674The number of hills of a Dyck path. St000093The cardinality of a maximal independent set of vertices of a graph. St000164The number of short pairs. St000291The number of descents of a binary word. St000413The number of ordered trees with the same underlying unordered tree. St000444The length of the maximal rise of a Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001058The breadth of the ordered tree. St000292The number of ascents of a binary word. St000340The number of non-final maximal constant sub-paths of length greater than one. St000895The number of ones on the main diagonal of an alternating sign matrix. St000157The number of descents of a standard tableau. St000460The hook length of the last cell along the main diagonal of an integer partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001360The number of covering relations in Young's lattice below a partition. St001378The product of the cohook lengths of the integer partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St000014The number of parking functions supported by a Dyck path. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000420The number of Dyck paths that are weakly above a Dyck path. St000504The cardinality of the first block of a set partition. St000529The number of permutations whose descent word is the given binary word. St000532The total number of rook placements on a Ferrers board. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000823The number of unsplittable factors of the set partition. 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. 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. St001400The total number of Littlewood-Richardson tableaux of given shape. St001658The total number of rook placements on a Ferrers board. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000038The product of the heights of the descending steps of a Dyck path. St000179The product of the hook lengths of the integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000228The size of a partition. St000335The difference of lower and upper interactions. St000418The number of Dyck paths that are weakly below a Dyck path. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000459The hook length of the base cell of a partition. St000519The largest length of a factor maximising the subword complexity. St000531The leading coefficient of the rook polynomial of an integer partition. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St000982The length of the longest constant subword. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in 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. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001488The number of corners of a skew partition. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001523The degree of symmetry of a Dyck path. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001531Number of partial orders contained in the poset determined by the Dyck path. St001612The number of coloured multisets of cycles such that the multiplicities of colours are given by a partition. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. 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. St001710The number of permutations such that conjugation with a permutation of given cycle type yields the inverse permutation. St001838The number of nonempty primitive factors of a binary word. St001959The product of the heights of the peaks of a Dyck path. St000012The area of a Dyck path. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000547The number of even non-empty partial sums of an integer partition. St000658The number of rises of length 2 of a Dyck path. St000659The number of rises of length at least 2 of a Dyck path. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000885The number of critical steps in the Catalan decomposition of a binary word. St000921The number of internal inversions of a binary word. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000984The number of boxes below precisely one peak. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001139The number of occurrences of hills of size 2 in a Dyck path. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001424The number of distinct squares in a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. 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). St001955The number of natural descents for set-valued two row standard Young tableaux. St000068The number of minimal elements in a poset. St000874The position of the last double rise in a Dyck path. St001733The number of weak left to right maxima of a Dyck path. St000546The number of global descents of a permutation. St000708The product of the parts of an integer partition. St000931The number of occurrences of the pattern UUU in a Dyck path. St001279The sum of the parts of an integer partition that are at least two. St001389The number of partitions of the same length below the given integer partition. St001809The index of the step at the first peak of maximal height in a Dyck path. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001118The acyclic chromatic index of a graph. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001759The Rajchgot index of a permutation. St000636The hull number of a graph. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001110The 3-dynamic chromatic number of a graph. St001654The monophonic hull number of a graph. St001725The harmonious chromatic number of a graph. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St000078The number of alternating sign matrices whose left key is the permutation. St000105The number of blocks in the set partition. St000171The degree of the graph. St000240The number of indices that are not small excedances. St000503The maximal difference between two elements in a common block. St000652The maximal difference between successive positions of a permutation. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000728The dimension of a set partition. St000730The maximal arc length of a set partition. St000868The aid statistic in the sense of Shareshian-Wachs. St001050The number of terminal closers of a set partition. St001081The number of minimal length factorizations of a permutation into star transpositions. St001120The length of a longest path in a graph. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. St001340The cardinality of a minimal non-edge isolating set of a graph. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St000025The number of initial rises of a Dyck path. St000047The number of standard immaculate tableaux of a given shape. St000118The number of occurrences of the contiguous pattern [.,[.,[.,.]]] in a binary tree. St000155The number of exceedances (also excedences) of a permutation. St000211The rank of the set partition. St000224The sorting index of a permutation. St000234The number of global ascents of a permutation. St000248The number of anti-singletons of a set partition. St000258The burning number of a graph. St000273The domination number of a graph. St000339The maf index of a permutation. St000424The number of occurrences of the pattern 132 or of the pattern 231 in a permutation. St000497The lcb statistic of a set partition. St000505The biggest entry in the block containing the 1. St000538The number of even inversions of a permutation. St000544The cop number of a graph. St000555The number of occurrences of the pattern {{1,3},{2}} in a set partition. St000572The dimension exponent of a set partition. St000582The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000600The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, (1,3) are consecutive in a block. St000602The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal. St000731The number of double exceedences of a permutation. St000795The mad of a permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000833The comajor index of a permutation. St000836The number of descents of distance 2 of a permutation. St000915The Ore degree of a graph. St000916The packing number of a graph. St000989The number of final rises of a permutation. St001268The size of the largest ordinal summand in the poset. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St001403The number of vertical separators in a permutation. St001647The number of edges that can be added without increasing the clique number. St001648The number of edges that can be added without increasing the chromatic number. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001727The number of invisible inversions of a permutation. St001779The order of promotion on the set of linear extensions of a poset. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001829The common independence number of a graph. St001841The number of inversions of a set partition. St001910The height of the middle non-run of a 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. St000702The number of weak deficiencies of a permutation. St000740The last entry of a permutation. St000482The (zero)-forcing number of a graph. St000654The first descent of a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001655The general position number of a graph. St001656The monophonic position number of a graph. St000653The last descent of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St001671Haglund's hag of a permutation. St000426The number of occurrences of the pattern 132 or of the pattern 312 in a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001379The number of inversions plus the major index of a permutation. St001461The number of topologically connected components of the chord diagram of a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St000255The number of reduced Kogan faces with the permutation as type. St000352The Elizalde-Pak rank of a permutation. St000470The number of runs in a permutation. St000794The mak of a permutation. St000354The number of recoils of a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000829The Ulam distance of a permutation to the identity permutation. St001489The maximum of the number of descents and the number of inverse descents. St001497The position of the largest weak excedence of a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St000838The number of terminal right-hand endpoints when the vertices are written in order. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000782The indicator function of whether a given perfect matching is an L & P matching. St000946The sum of the skew hook positions in a Dyck path. St000542The number of left-to-right-minima of a permutation. St000619The number of cyclic descents of a permutation. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000864The number of circled entries of the shifted recording tableau of a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St000316The number of non-left-to-right-maxima of a permutation. St000991The number of right-to-left minima of a permutation. St001117The game chromatic index of a graph. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000222The number of alignments in the permutation. St000338The number of pixed points of a permutation. St000471The sum of the ascent tops of a permutation. St000004The major index of a permutation. St000021The number of descents of a permutation. St000051The size of the left subtree of a binary tree. St000056The decomposition (or block) number of a permutation. St000061The number of nodes on the left branch of a binary tree. St000067The inversion number of the alternating sign matrix. St000083The number of left oriented leafs of a binary tree except the first one. St000084The number of subtrees. St000089The absolute variation of a composition. St000156The Denert index of a permutation. St000238The number of indices that are not small weak excedances. St000304The load of a permutation. St000305The inverse major index of a permutation. St000325The width of the tree associated to a permutation. St000328The maximum number of child nodes in a tree. St000389The number of runs of ones of odd length in a binary word. St000638The number of up-down runs of a permutation. St000886The number of permutations with the same antidiagonal sums. St000990The first ascent of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. 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. 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. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001530The depth of a Dyck path. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001869The maximum cut size of a graph. St000039The number of crossings of a permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000120The number of left tunnels of a Dyck path. St000168The number of internal nodes of an ordered tree. St000235The number of indices that are not cyclical small weak excedances. St000236The number of cyclical small weak excedances. St000241The number of cyclical small excedances. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000287The number of connected components of a graph. St000332The positive inversions of an alternating sign matrix. St000365The number of double ascents of a permutation. St000427The number of occurrences of the pattern 123 or of the pattern 231 in a permutation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000800The number of occurrences of the vincular pattern |231 in a permutation. St001083The number of boxed occurrences of 132 in a permutation. 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. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. 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. St001388The number of non-attacking neighbors of a permutation. St001498The normalised height of a Nakayama algebra with magnitude 1. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001684The reduced word complexity of a permutation. St001828The Euler characteristic of a graph. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St000454The largest eigenvalue of a graph if it is integral. St000706The product of the factorials of the multiplicities of an integer partition. St000993The multiplicity of the largest part of an integer partition. St001568The smallest positive integer that does not appear twice in the partition. St000567The sum of the products of all pairs of parts. St000929The constant term of the character polynomial of an integer partition. St001099The 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 leaf labelled binary trees. St001100The 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 leaf labelled trees. 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. St001519The pinnacle sum of a permutation. St000961The shifted major index of a permutation. St000462The major index minus the number of excedences of a permutation. St000488The number of cycles of a permutation of length at most 2. St000726The normalized sum of the leaf labels of the increasing binary tree associated to a permutation. St000894The trace of an alternating sign matrix. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001330The hat guessing number of a graph. St000898The number of maximal entries in the last diagonal of the monotone triangle. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001948The number of augmented double ascents of a permutation. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000200The row of the unique '1' in the last column of the alternating sign matrix. St000317The cycle descent number of a permutation. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St001557The number of inversions of the second entry of a permutation. St001566The length of the longest arithmetic progression in a permutation. St001569The maximal modular displacement of a permutation. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. 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. St000707The product of the factorials of the parts. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000933The number of multipartitions of sizes given by an integer partition. St001128The exponens consonantiae of a partition. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St000477The weight of a partition according to Alladi. St000509The diagonal index (content) of a partition. St000928The sum of the coefficients of the character polynomial of an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000681The Grundy value of Chomp on Ferrers diagrams. St000937The number of positive values of the symmetric group character corresponding to the partition. St000284The Plancherel distribution on integer partitions. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000735The last entry on the main diagonal of a standard tableau. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000661The number of rises of length 3 of a Dyck path. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001141The number of occurrences of hills of size 3 in a Dyck path. St001863The number of weak excedances of a signed permutation. St001060The distinguishing index of a graph. St000260The radius of a connected graph. St000770The major index of an integer partition when read from bottom to top. St000815The number of semistandard Young tableaux of partition weight of given shape. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000478Another weight of a partition according to Alladi. St000934The 2-degree of an integer partition. St000942The number of critical left to right maxima of the parking functions. St001712The number of natural descents of a standard Young tableau. St000264The girth of a graph, which is not a tree. St000766The number of inversions of an integer composition. St001861The number of Bruhat lower covers of a permutation. St001875The number of simple modules with projective dimension at most 1. St001894The depth of a signed permutation. St001935The number of ascents in a parking function. St000456The monochromatic index of a connected graph. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001822The number of alignments of a signed permutation. St001866The nesting alignments of a signed permutation. St001903The number of fixed points of a parking function. St000422The energy of a graph, if it is integral. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001820The size of the image of the pop stack sorting operator. St001720The minimal length of a chain of small intervals in a lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001098The 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 vertex labelled trees. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000927The alternating sum of the coefficients of the character polynomial of an integer partition. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St000997The even-odd crank of an integer partition. St000716The dimension of the irreducible representation of Sp(6) labelled by an integer partition. St001877Number of indecomposable injective modules with projective dimension 2. St000522The number of 1-protected nodes of a rooted tree. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. 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 $eA$. 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 $eA$. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000137The Grundy value of an integer partition. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000521The number of distinct subtrees of an ordered tree. St000618The number of self-evacuating tableaux of given shape. St000667The greatest common divisor of the parts of the partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000781The number of proper colouring schemes of a Ferrers diagram. St000973The length of the boundary of an ordered tree. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a 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. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001383The BG-rank of an integer partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001525The number of symmetric hooks on the diagonal of a partition. St001527The cyclic permutation representation number of an integer partition. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition. St001561The value of the elementary symmetric function evaluated at 1. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001571The Cartan determinant of the integer partition. St001593This is the number of standard Young tableaux of the given shifted shape. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001610The number of coloured endofunctions such that the multiplicities of colours are given by a partition. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001763The Hurwitz number of an integer partition. St001780The order of promotion on the set of standard tableaux of given shape. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001943The sum of the squares of the hook lengths of an integer partition. St000145The Dyson rank of a partition. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000944The 3-degree of an integer partition. St001175The size of a partition minus the hook length of the base cell. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001248Sum of the even parts of a partition. St001280The number of parts of an integer partition that are at least two. St001541The Gini index of an integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001587Half of the largest even part of an integer partition. St001657The number of twos in an integer partition. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St000474Dyson's crank of a partition. St000307The number of rowmotion orbits of a poset. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000834The number of right outer peaks of a permutation. 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. St000741The Colin de Verdière graph invariant. St001964The interval resolution global dimension of a poset.