St000385The number of vertices with out-degree 1 in a binary tree. St000393The number of strictly increasing runs in a binary word. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000519The largest length of a factor maximising the subword complexity. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000806The semiperimeter of the associated bargraph. St000876The number of factors in the Catalan decomposition of a binary word. St000885The number of critical steps in the Catalan decomposition of a binary word. St001034The area of the parallelogram polyomino associated with the Dyck path. St001267The length of the Lyndon factorization of the binary word. St001437The flex of a binary word. St000060The greater neighbor of the maximum. St000543The size of the conjugacy class of a binary word. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St000203The number of external nodes of a binary tree. St000294The number of distinct factors of a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000395The sum of the heights of the peaks of a Dyck path. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000518The number of distinct subsequences in a binary word. St000528The height of a poset. St000548The number of different non-empty partial sums of an integer partition. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000738The first entry in the last row of a standard tableau. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000907The number of maximal antichains of minimal length in a poset. St000911The number of maximal antichains of maximal size in a poset. St000912The number of maximal antichains in a poset. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001093The detour number of a graph. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001342The number of vertices in the center of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001371The length of the longest Yamanouchi prefix of a binary word. St001523The degree of symmetry of a Dyck path. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001746The coalition number of a graph. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000018The number of inversions of a permutation. St000070The number of antichains in a poset. St000081The number of edges of a graph. St000246The number of non-inversions of a permutation. St000259The diameter of a connected graph. St000290The major index of a binary word. St000296The length of the symmetric border of a binary word. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000553The number of blocks of a graph. St000625The sum of the minimal distances to a greater element. St000627The exponent of a binary word. St000657The smallest part of an integer composition. St000734The last entry in the first row of a standard tableau. St000808The number of up steps of the associated bargraph. St000922The minimal number such that all substrings of this length are unique. St000982The length of the longest constant subword. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. 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. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001074The number of inversions of the cyclic embedding of a permutation. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001176The size of a partition minus its first part. St001332The number of steps on the non-negative side of the walk associated with the permutation. 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. St001479The number of bridges of a graph. St001485The modular major index of a binary word. St001512The minimum rank of a graph. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. 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. St001884The number of borders of a binary word. St001917The order of toric promotion on the set of labellings of a graph. St000295The length of the border of a binary word. St000313The number of degree 2 vertices of a graph. St000448The number of pairs of vertices of a graph with distance 2. St000552The number of cut vertices of a graph. St000626The minimal period of a binary word. St000867The sum of the hook lengths in the first row of an integer partition. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001308The number of induced paths on three vertices in a graph. St001368The number of vertices of maximal degree in a graph. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001521Half the total irregularity of a graph. St001692The number of vertices with higher degree than the average degree in a graph. St000447The number of pairs of vertices of a graph with distance 3. St001306The number of induced paths on four vertices in a graph. St001279The sum of the parts of an integer partition that are at least two. St000975The length of the boundary minus the length of the trunk of an ordered tree. St000019The cardinality of the support of a permutation. St000271The chromatic index of a graph. St000050The depth or height of a binary tree. St000505The biggest entry in the block containing the 1. St000653The last descent of a permutation. St001497The position of the largest weak excedence of a permutation. St000503The maximal difference between two elements in a common block. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St001622The number of join-irreducible elements of a lattice. St000245The number of ascents of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St001759The Rajchgot index of a permutation. St000054The first entry of the permutation. St000141The maximum drop size of a permutation. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001955The number of natural descents for set-valued two row standard Young tableaux. St000839The largest opener of a set partition. St001430The number of positive entries in a signed permutation. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000288The number of ones in a binary word. St000336The leg major index of a standard tableau. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St001958The degree of the polynomial interpolating the values of a permutation. St000863The length of the first row of the shifted shape of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St001018Sum of projective dimension of the indecomposable injective modules of 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. St000189The number of elements in the poset. St000636The hull number of a graph. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St000144The pyramid weight of the Dyck path. St000171The degree of the graph. St000299The number of nonisomorphic vertex-induced subtrees. St000363The number of minimal vertex covers of a graph. St000501The size of the first part in the decomposition of a permutation. St000656The number of cuts of a poset. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000730The maximal arc length of a set partition. St000844The size of the largest block in the direct sum decomposition of a permutation. St000906The length of the shortest maximal chain in a poset. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001717The largest size of an interval in a poset. St001883The mutual visibility number of a graph. St000026The position of the first return of a Dyck path. St000080The rank of the poset. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St000167The number of leaves of an ordered tree. St000209Maximum difference of elements in cycles. St000213The number of weak exceedances (also weak excedences) of a permutation. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000316The number of non-left-to-right-maxima of a permutation. St000362The size of a minimal vertex cover of a graph. St000383The last part of an integer composition. St000619The number of cyclic descents of a permutation. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000702The number of weak deficiencies of a permutation. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000722The number of different neighbourhoods in a graph. St000956The maximal displacement of a permutation. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. 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. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001246The maximal difference between two consecutive entries of a permutation. St001391The disjunction number of a graph. St001463The number of distinct columns in the nullspace of a graph. 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. St001516The number of cyclic bonds of a permutation. St001580The acyclic chromatic number of a graph. St001649The length of a longest trail in a graph. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001664The number of non-isomorphic subposets of a poset. St001672The restrained domination number of a graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001782The order of rowmotion on the set of order ideals of a poset. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St000242The number of indices that are not cyclical small weak excedances. St000272The treewidth of a graph. St000309The number of vertices with even degree. St000354The number of recoils of a permutation. St000536The pathwidth of a graph. St000829The Ulam distance of a permutation to the identity permutation. St000836The number of descents of distance 2 of a permutation. 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. St001489The maximum of the number of descents and the number of inverse descents. St000010The length of the partition. St001268The size of the largest ordinal summand in the poset. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000837The number of ascents of distance 2 of a permutation. St001645The pebbling number of a connected graph. St000058The order of a permutation. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000740The last entry of a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St000890The number of nonzero entries in an alternating sign matrix. St001925The minimal number of zeros in a row of an alternating sign matrix. St001725The harmonious chromatic number of a graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000719The number of alignments in a perfect matching. St000784The maximum of the length and the largest part of the integer partition. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St000924The number of topologically connected components of a perfect matching. St000651The maximal size of a rise in a permutation. St000454The largest eigenvalue of a graph if it is integral. St000197The number of entries equal to positive one in the alternating sign matrix. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001557The number of inversions of the second entry of a permutation. St001556The number of inversions of the third entry of a permutation. St000051The size of the left subtree of a binary tree. St000052The number of valleys of a Dyck path not on the x-axis. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. St000652The maximal difference between successive positions of a permutation. St000957The number of Bruhat lower covers of a permutation. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001077The prefix exchange distance of a permutation. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001304The number of maximally independent sets of vertices of a graph. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001480The number of simple summands of the module J^2/J^3. St001963The tree-depth of a graph. St000028The number of stack-sorts needed to sort a permutation. St000031The number of cycles in the cycle decomposition 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. St000235The number of indices that are not cyclical small weak excedances. St000240The number of indices that are not small excedances. St000304The load of a permutation. St000327The number of cover relations in a poset. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000632The jump number of the poset. St000673The number of non-fixed points of a permutation. St000703The number of deficiencies of a permutation. St000733The row containing the largest entry of a standard tableau. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000822The Hadwiger number of the graph. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001052The length of the exterior of a permutation. St001096The size of the overlap set of a permutation. St001118The acyclic chromatic index of a graph. 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. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001566The length of the longest arithmetic progression in a permutation. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001760The number of prefix or suffix reversals needed to sort a permutation. St000068The number of minimal elements in a poset. St000071The number of maximal chains in a poset. St000312The number of leaves in a graph. St000451The length of the longest pattern of the form k 1 2. St000456The monochromatic index of a connected graph. St000527The width of the poset. St000864The number of circled entries of the shifted recording tableau of a permutation. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001277The degeneracy of a graph. St001468The smallest fixpoint 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. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. 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. St001520The number of strict 3-descents. St000066The column of the unique '1' in the first row of the alternating sign matrix. 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. St000147The largest part of an integer partition. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001875The number of simple modules with projective dimension at most 1. St000093The cardinality of a maximal independent set of vertices of a graph. St001060The distinguishing index of a graph. St001401The number of distinct entries in a semistandard tableau. St000135The number of lucky cars of the parking function. St001927Sparre Andersen's number of positives of a signed permutation. St001429The number of negative entries in a signed permutation. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000095The number of triangles of a graph. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000744The length of the path to the largest entry in a standard Young tableau. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001742The difference of the maximal and the minimal degree in a graph. St000029The depth of a permutation. St000044The number of vertices of the unicellular map given by a perfect matching. St000067The inversion number of the alternating sign matrix. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000450The number of edges minus the number of vertices plus 2 of a graph. St000809The reduced reflection length of the permutation. St001045The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001117The game chromatic index of a graph. St001132The number of leaves in the subtree whose sister has label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001511The minimal number of transpositions needed to sort a permutation in either direction. 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. St001703The villainy of a graph. St001734The lettericity of a graph. 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). St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001706The number of closed sets in a graph. St001817The number of flag weak exceedances of a signed permutation. St001892The flag excedance statistic of a signed permutation. St000137The Grundy value of an integer partition. St001383The BG-rank of an integer partition. St000533The minimum of the number of parts and the size of the first part of an integer partition. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001462The number of factors of a standard tableaux under concatenation. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000391The sum of the positions of the ones in a binary word. St001330The hat guessing number of a graph. St000522The number of 1-protected nodes of a rooted tree. St001434The number of negative sum pairs of a signed permutation. St000521The number of distinct subtrees of an ordered tree. St001820The size of the image of the pop stack sorting operator. St001720The minimal length of a chain of small intervals in a lattice. 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. St001488The number of corners of a skew partition. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St001845The number of join irreducibles minus the rank of a lattice. St000225Difference between largest and smallest parts in a partition. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St001340The cardinality of a minimal non-edge isolating set of a graph. St000273The domination number of a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000916The packing number of a graph. St000917The open packing number of a graph. 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. St001829The common independence number of a graph. St000449The number of pairs of vertices of a graph with distance 4. St000778The metric dimension of a graph. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St001029The size of the core of a graph. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001494The Alon-Tarsi number of a graph. St001623The number of doubly irreducible elements of a lattice. St001316The domatic number of a graph. St000422The energy of a graph, if it is integral. St001626The number of maximal proper sublattices of a lattice.