St000459The hook length of the base cell of a partition. St000460The hook length of the last cell along the main diagonal of an integer partition. St000469The distinguishing number of a graph. St000518The number of distinct subsequences in a binary word. St000531The leading coefficient of the rook polynomial of an integer partition. St000548The number of different non-empty partial sums of an integer partition. St000636The hull number of a graph. St000784The maximum of the length and the largest part of the integer partition. St000839The largest opener of a set partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000926The clique-coclique number of a graph. St001034The area of the parallelogram polyomino associated with the Dyck path. St001267The length of the Lyndon factorization of the binary word. 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. St001360The number of covering relations in Young's lattice below a partition. St001437The flex of a binary word. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. 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. St000063The number of linear extensions of a certain poset defined for an integer partition. St000081The number of edges of a graph. St000108The number of partitions contained in the given partition. St000296The length of the symmetric border of a binary word. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000519The largest length of a factor maximising the subword complexity. St000532The total number of rook placements on a Ferrers board. St000553The number of blocks of a graph. St000627The exponent of a binary word. St000651The maximal size of a rise in a permutation. St000681The Grundy value of Chomp on Ferrers diagrams. St000778The metric dimension of a graph. 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. 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. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001279The sum of the parts of an integer partition that are at least two. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001371The length of the longest Yamanouchi prefix of a binary word. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001400The total number of Littlewood-Richardson tableaux of given shape. 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. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001658The total number of rook placements on a Ferrers board. St001884The number of borders of a binary word. St001949The rigidity index of a graph. St000019The cardinality of the support of a permutation. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000295The length of the border of a binary word. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St000013The height of a Dyck path. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000293The number of inversions of a binary word. St000326The position of the first one in a binary word after appending a 1 at the end. St000505The biggest entry in the block containing the 1. St000528The height of a poset. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000722The number of different neighbourhoods in a graph. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. 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. St000738The first entry in the last row of a standard tableau. St000740The last entry of a permutation. St000825The sum of the major and the inverse major index of a permutation. 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. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001249Sum of the odd parts of a partition. St001343The dimension of the reduced incidence algebra of a poset. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. 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. St001497The position of the largest weak excedence of a permutation. St001523The degree of symmetry of a Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. St001622The number of join-irreducible elements of a lattice. St001672The restrained domination number of a graph. St001746The coalition number of a graph. St001778The largest greatest common divisor of an element and its image in a permutation. St001838The number of nonempty primitive factors of a binary word. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000031The number of cycles in the cycle decomposition of a permutation. St000058The order of a permutation. St000070The number of antichains in a poset. St000078The number of alternating sign matrices whose left key is the permutation. St000110The number of permutations less than or equal to a permutation in left weak order. St000189The number of elements in the poset. St000255The number of reduced Kogan faces with the permutation as type. St000363The number of minimal vertex covers of a graph. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000385The number of vertices with out-degree 1 in a binary tree. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000451The length of the longest pattern of the form k 1 2. St000501The size of the first part in the decomposition of a permutation. St000503The maximal difference between two elements in a common block. St000529The number of permutations whose descent word is the given binary word. St000657The smallest part of an integer composition. St000692Babson and Steingrímsson's statistic of a permutation. St000696The number of cycles in the breakpoint graph of a permutation. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000744The length of the path to the largest entry in a standard Young tableau. St000808The number of up steps of the associated bargraph. St000820The number of compositions obtained by rotating the composition. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. St000844The size of the largest block in the direct sum decomposition of a permutation. St000867The sum of the hook lengths in the first row of an integer partition. St000877The depth of the binary word interpreted as a path. St000921The number of internal inversions of a binary word. St000983The length of the longest alternating subword. St001007Number of simple modules with projective dimension 1 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. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001090The number of pop-stack-sorts needed to sort a permutation. 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. St001176The size of a partition minus its first part. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001430The number of positive entries in a signed permutation. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. 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. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St001759The Rajchgot index 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. St001955The number of natural descents for set-valued two row standard Young tableaux. St000018The number of inversions of a permutation. St000022The number of fixed points of a permutation. St000024The number of double up and double down steps of a Dyck path. St000141The maximum drop size of a permutation. St000157The number of descents of a standard tableau. St000171The degree of the graph. St000209Maximum difference of elements in cycles. St000220The number of occurrences of the pattern 132 in a permutation. St000245The number of ascents of a permutation. St000288The number of ones in a binary word. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000356The number of occurrences of the pattern 13-2. St000362The size of a minimal vertex cover of a graph. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000433The number of occurrences of the pattern 132 or of the pattern 321 in a permutation. St000441The number of successions of a permutation. St000457The number of occurrences of one of the patterns 132, 213 or 321 in a permutation. St000463The number of admissible inversions of a permutation. St000619The number of cyclic descents of a permutation. St000653The last descent of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000691The number of changes of a binary word. St000703The number of deficiencies of a permutation. St000776The maximal multiplicity of an eigenvalue in a graph. St000904The maximal number of repetitions of an integer composition. St000956The maximal displacement of a permutation. St001082The number of boxed occurrences of 123 in a permutation. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001246The maximal difference between two consecutive entries of a permutation. St001372The length of a longest cyclic run of ones of a binary word. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001958The degree of the polynomial interpolating the values of a permutation. St000242The number of indices that are not cyclical small weak excedances. St000878The number of ones minus the number of zeros of a binary word. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000007The number of saliances of the permutation. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000632The jump number of the poset. St000662The staircase size of the code of a permutation. St000809The reduced reflection length of the permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000957The number of Bruhat lower covers of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001298The number of repeated entries in the Lehmer code of a permutation. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001726The number of visible inversions of a permutation. St000366The number of double descents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. 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. St001120The length of a longest path in a graph. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000054The first entry of the permutation. St001645The pebbling number of a connected graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St000010The length of the partition. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000147The largest part of an integer partition. St001268The size of the largest ordinal summand in the poset. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001917The order of toric promotion on the set of labellings of a graph. St000656The number of cuts of a poset. St000050The depth or height of a binary tree. St000336The leg major index of a standard tableau. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St000890The number of nonzero entries in an alternating sign matrix. St001925The minimal number of zeros in a row of an alternating sign matrix. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St000093The cardinality of a maximal independent set of vertices of a graph. St000028The number of stack-sorts needed to sort a permutation. St000163The size of the orbit of the set partition under rotation. 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. St001286The annihilation 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. St000259The diameter of a connected graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St000271The chromatic index of a graph. St001820The size of the image of the pop stack sorting operator. St001720The minimal length of a chain of small intervals in a lattice. St000728The dimension of a set partition. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001725The harmonious chromatic number of a graph. St000733The row containing the largest entry of a standard tableau. St000225Difference between largest and smallest parts in a partition. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000444The length of the maximal rise of a Dyck path. St000625The sum of the minimal distances to a greater element. St000863The length of the first row of the shifted shape of a permutation. St001074The number of inversions of the cyclic embedding of a permutation. St000420The number of Dyck paths that are weakly above a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St000931The number of occurrences of the pattern UUU in a Dyck path. St000144The pyramid weight of the Dyck path. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. 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 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. St000087The number of induced subgraphs. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000240The number of indices that are not small excedances. St000471The sum of the ascent tops of a permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001052The length of the exterior of a permutation. St001096The size of the overlap set of a permutation. 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. St000051The size of the left subtree of a binary tree. St000060The greater neighbor of the maximum. St000167The number of leaves of an ordered tree. St000316The number of non-left-to-right-maxima of a permutation. St000325The width of the tree associated to a permutation. St000470The number of runs in a permutation. St000652The maximal difference between successive positions 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. St001225The vector space dimension of the first extension group between J and itself when J is 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. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001480The number of simple summands of the module J^2/J^3. St001516The number of cyclic bonds of a permutation. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St000021The number of descents of a permutation. St000030The sum of the descent differences of a permutations. St000238The number of indices that are not small weak excedances. St000354The number of recoils of a permutation. St000795The mad of a permutation. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St001061The number of indices that are both descents and recoils of a permutation. St001405The number of bonds in a permutation. St001489The maximum of the number of descents and the number of inverse descents. St000064The number of one-box pattern of a permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000111The sum of the descent tops (or Genocchi descents) of a permutation. St000235The number of indices that are not cyclical small weak excedances. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. 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. St000680The Grundy value for Hackendot on posets. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000717The number of ordinal summands of a poset. St000906The length of the shortest maximal chain in a poset. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001077The prefix exchange distance of a permutation. St001118The acyclic chromatic index of a graph. St001180Number of indecomposable injective modules with projective dimension at most 1. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001252Half the sum of the even parts of a partition. St001379The number of inversions plus the major index of a permutation. St001439The number of even weak deficiencies and of odd weak exceedences. St001519The pinnacle sum of a permutation. St001717The largest size of an interval in a poset. St001883The mutual visibility number of a graph. St000052The number of valleys of a Dyck path not on the x-axis. St000062The length of the longest increasing subsequence of the permutation. St000067The inversion number of the alternating sign matrix. St000068The number of minimal elements in a poset. St000071The number of maximal chains in a poset. St000080The rank of the poset. St000104The number of facets in the order polytope of this poset. St000133The "bounce" of a permutation. St000151The number of facets in the chain polytope of the poset. St000197The number of entries equal to positive one in the alternating sign matrix. St000210Minimum over maximum difference of elements in cycles. St000213The number of weak exceedances (also weak excedences) of a permutation. St000216The absolute length of a permutation. St000304The load of a permutation. St000305The inverse major index of a permutation. St000308The height of the tree associated to a permutation. St000312The number of leaves in a graph. St000443The number of long tunnels of a Dyck path. St000456The monochromatic index of a connected graph. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000527The width of the poset. St000530The number of permutations with the same descent word as the given permutation. St000542The number of left-to-right-minima 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. St000797The stat`` of a permutation. St000798The makl of a permutation. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000990The first ascent of a permutation. St000991The number of right-to-left minima of a permutation. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001081The number of minimal length factorizations of a permutation into star transpositions. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in 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. 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. St001356The number of vertices in prime modules of a graph. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001391The disjunction number of a graph. St001461The number of topologically connected components of the chord diagram of a permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001468The smallest fixpoint of a permutation. St001566The length of the longest arithmetic progression in a permutation. St001664The number of non-isomorphic subposets of a poset. St001671Haglund's hag of a permutation. St001782The order of rowmotion on the set of order ideals of a poset. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St001963The tree-depth of a graph. St000029The depth of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000222The number of alignments in the permutation. St000224The sorting index of a permutation. St000237The number of small exceedances. St000241The number of cyclical small excedances. St000301The number of facets of the stable set polytope of a graph. St000331The number of upper interactions of a Dyck path. St000424The number of occurrences of the pattern 132 or of the pattern 231 in a permutation. St000425The number of occurrences of the pattern 132 or of the pattern 213 in a permutation. St000461The rix statistic of a permutation. St000495The number of inversions of distance at most 2 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. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000833The comajor index of a permutation. St000837The number of ascents of distance 2 of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001160The number of proper blocks (or intervals) of a permutations. 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. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001427The number of descents of a signed permutation. 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. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001760The number of prefix or suffix reversals needed to sort a permutation. St001812The biclique partition number of a graph. St001911A descent variant minus the number of inversions. St000317The cycle descent number of a permutation. St000358The number of occurrences of the pattern 31-2. St000732The number of double deficiencies of a permutation. St000989The number of final rises of a permutation. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001727The number of invisible inversions of a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St000924The number of topologically connected components of a perfect matching. St000840The number of closers smaller than the largest opener in a perfect matching. St000454The largest eigenvalue of a graph if it is integral. St000898The number of maximal entries in the last diagonal of the monotone triangle. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St001136The largest label with larger sister in the leaf labelled binary unordered tree associated with the perfect matching. St001809The index of the step at the first peak of maximal height in a Dyck path. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St001875The number of simple modules with projective dimension at most 1. 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. St000246The number of non-inversions of a permutation. St000883The number of longest increasing subsequences of a permutation. St001029The size of the core of a graph. St001108The 2-dynamic chromatic number of a graph. St001494The Alon-Tarsi number of a graph. St000549The number of odd partial sums of an integer partition. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000200The row of the unique '1' in the last column of the alternating sign matrix. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St000327The number of cover relations in a poset. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001520The number of strict 3-descents. St001556The number of inversions of the third entry of a permutation. St000004The major index of a permutation. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000332The positive inversions of an alternating sign matrix. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000335The difference of lower and upper interactions. St000450The number of edges minus the number of vertices plus 2 of a graph. St000547The number of even non-empty partial sums of an integer partition. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000896The number of zeros on the main diagonal of an alternating sign matrix. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St001045The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching. 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. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. 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 $eA$. 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. St001238The number of simple modules S such that the Auslander-Reiten translate of S is isomorphic to the Nakayama functor applied to the second syzygy of S. 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. St001397Number of pairs of incomparable elements in a finite poset. St001428The number of B-inversions of a signed permutation. St001429The number of negative entries in a signed permutation. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001959The product of the heights of the peaks of a Dyck path. St000014The number of parking functions supported by a Dyck path. St000015The number of peaks of a Dyck path. St000095The number of triangles of a graph. St000231Sum of the maximal elements of the blocks of a set partition. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000836The number of descents of distance 2 of a permutation. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. 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 $eA$. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive. St001228The vector space dimension of the space of module homomorphisms between J and itself when J denotes the Jacobson radical of the corresponding Nakayama algebra. St001254The vector space dimension of the first extension-group between A/soc(A) and J when A is the corresponding Nakayama algebra with Jacobson radical J. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001263The index of the maximal parabolic seaweed algebra associated with the composition. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001524The degree of symmetry of a binary word. St001530The depth of a Dyck path. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001927Sparre Andersen's number of positives of a signed permutation. St000005The bounce statistic of a Dyck path. St000968We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n−1}]$ by adding $c_0$ to $c_{n−1}$. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001256Number of simple reflexive modules that are 2-stable reflexive. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001557The number of inversions of the second entry of a permutation. St001684The reduced word complexity of a permutation. St001742The difference of the maximal and the minimal degree in a graph. St001960The number of descents of a permutation minus one if its first entry is not one. St001706The number of closed sets in a graph. St001138The number of indecomposable modules with projective dimension or injective dimension at most one in the corresponding Nakayama algebra. St001817The number of flag weak exceedances of a signed permutation. St001892The flag excedance statistic of a signed permutation. St001434The number of negative sum pairs of a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001896The number of right descents of a signed permutations. St001330The hat guessing number of a graph. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001644The dimension of a graph.