St000507The number of ascents of a standard tableau. St000553The number of blocks of a graph. St000625The sum of the minimal distances to a greater element. St000863The length of the first row of the shifted shape of a permutation. St000876The number of factors in the Catalan decomposition of a binary word. St000885The number of critical steps in the Catalan decomposition of a binary word. 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. 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. 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. St001479The number of bridges of a graph. St001512The minimum rank of a graph. St001641The number of ascent tops in the flattened set partition such that all smaller elements appear before. St001917The order of toric promotion on the set of labellings of a graph. St000026The position of the first return of a Dyck path. St000228The size of a partition. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000313The number of degree 2 vertices of a graph. St000448The number of pairs of vertices of a graph with distance 2. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. 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. St000519The largest length of a factor maximising the subword complexity. St000552The number of cut vertices of a graph. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000839The largest opener of a set partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001034The area of the parallelogram polyomino associated with the Dyck path. St001093The detour number of a graph. St001176The size of a partition minus its first part. St001308The number of induced paths on three vertices in a graph. 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. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001368The number of vertices of maximal degree in 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. St001521Half the total irregularity of a graph. St001554The number of distinct nonempty subtrees of a binary tree. St001692The number of vertices with higher degree than the average degree in a graph. 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. St000447The number of pairs of vertices of a graph with distance 3. St000806The semiperimeter of the associated bargraph. St000867The sum of the hook lengths in the first row of an integer partition. 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. St001306The number of induced paths on four vertices in a graph. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St000003The number of standard Young tableaux of the partition. St000010The length of the partition. St000053The number of valleys of the Dyck path. St000144The pyramid weight of the Dyck path. St000189The number of elements in the poset. St000203The number of external nodes of a binary tree. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000296The length of the symmetric border of a binary word. St000363The number of minimal vertex covers of a graph. St000377The dinv defect of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000393The number of strictly increasing runs in a binary word. St000501The size of the first part in the decomposition of a permutation. St000503The maximal difference between two elements in a common block. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000627The exponent of a binary word. St000676The number of odd rises of a Dyck path. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000738The first entry in the last row of a standard tableau. St000784The maximum of the length and the largest part of the integer partition. 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. St000877The depth of the binary word interpreted as a path. St000921The number of internal inversions of a binary word. St000922The minimal number such that all substrings of this length are unique. St000932The number of occurrences of the pattern UDU in a Dyck path. St000982The length of the longest constant subword. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001267The length of the Lyndon factorization of the binary word. 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. St001430The number of positive entries in a signed permutation. St001437The flex of a binary word. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001541The Gini index of an integer partition. 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. St001721The degree of a binary word. St001777The number of weak descents in an integer composition. St001780The order of promotion on the set of standard tableaux of given shape. 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. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001955The number of natural descents for set-valued two row standard Young tableaux. St000011The number of touch points (or returns) of a Dyck path. St000019The cardinality of the support of a permutation. St000024The number of double up and double down steps of a Dyck path. St000058The order of a permutation. St000060The greater neighbor of the maximum. St000088The row sums of the character table of the symmetric group. St000145The Dyson rank of a partition. St000148The number of odd parts of a partition. St000157The number of descents of a standard tableau. St000160The multiplicity of the smallest part of a partition. St000171The degree of the graph. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000209Maximum difference of elements in cycles. St000211The rank of the set partition. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000248The number of anti-singletons of a set partition. St000271The chromatic index of a graph. St000288The number of ones in a binary word. St000293The number of inversions of a binary word. St000294The number of distinct factors of a binary word. St000295The length of the border of a binary word. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000326The position of the first one in a binary word after appending a 1 at the end. St000362The size of a minimal vertex cover of a graph. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000445The number of rises of length 1 of a Dyck path. St000475The number of parts equal to 1 in a partition. St000502The number of successions of a set partitions. St000505The biggest entry in the block containing the 1. St000518The number of distinct subsequences in a binary word. St000528The height of a poset. St000531The leading coefficient of the rook polynomial of an integer partition. St000548The number of different non-empty partial sums of an integer partition. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000636The hull number of a graph. St000653The last descent of a permutation. St000674The number of hills of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000681The Grundy value of Chomp on Ferrers diagrams. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000722The number of different neighbourhoods in a graph. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000728The dimension of a set partition. St000734The last entry in the first row of a standard tableau. St000740The last entry of a permutation. St000743The number of entries in a standard Young tableau such that the next integer is a neighbour. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000815The number of semistandard Young tableaux of partition weight of given shape. St000899The maximal number of repetitions of an integer composition. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000904The maximal number of repetitions of an integer composition. 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. St000956The maximal displacement of a permutation. St000975The length of the boundary minus the length of the trunk of an ordered tree. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001063Numbers of 3-torsionfree simple modules in the corresponding Nakayama algebra. St001064Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy modules. St001082The number of boxed occurrences of 123 in a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive 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: 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. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001342The number of vertices in the center of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001372The length of a longest cyclic run of ones of a binary word. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001497The position of the largest weak excedence of a permutation. St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St001523The degree of symmetry of a Dyck path. St001586The number of odd parts smaller than the largest even part in an integer partition. St001622The number of join-irreducible elements of a lattice. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. 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. St001672The restrained domination number of a graph. St001675The number of parts equal to the part in the reversed composition. St001688The sum of the squares of the heights of the peaks of a Dyck path. St001694The number of maximal dissociation sets in a graph. St001733The number of weak left to right maxima of a Dyck path. St001746The coalition number of a graph. St001778The largest greatest common divisor of an element and its image in a permutation. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001933The largest multiplicity of a part in an integer partition. St001958The degree of the polynomial interpolating the values of a permutation. St000070The number of antichains in a poset. St000147The largest part of an integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000474Dyson's crank of a partition. St000477The weight of a partition according to Alladi. St000504The cardinality of the first block of a set partition. St000667The greatest common divisor of the parts of the partition. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000770The major index of an integer partition when read from bottom to top. St000823The number of unsplittable factors of the set partition. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000878The number of ones minus the number of zeros of a binary word. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. St000971The smallest closer of a set partition. St000992The alternating sum of the parts of an integer partition. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001062The maximal size of a block of a set partition. St001075The minimal size of a block of a set partition. St001091The number of parts in an integer partition whose next smaller part has the same size. 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. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001360The number of covering relations in Young's lattice below a partition. St001389The number of partitions of the same length below the given integer partition. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001527The cyclic permutation representation number of an integer partition. St001571The Cartan determinant of the integer partition. St001723The differential of a graph. St001724The 2-packing differential of a graph. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000532The total number of rook placements on a Ferrers board. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St001127The sum of the squares of the parts of a partition. St001400The total number of Littlewood-Richardson tableaux of given shape. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001814The number of partitions interlacing the given partition. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St000028The number of stack-sorts needed to sort a permutation. St000463The number of admissible inversions of a permutation. St000651The maximal size of a rise in a permutation. St000696The number of cycles in the breakpoint graph of a permutation. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000245The number of ascents of a permutation. St000517The Kreweras number of an integer partition. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St000018The number of inversions of a permutation. St000141The maximum drop size of a permutation. St000054The first entry of the permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St000702The number of weak deficiencies of a permutation. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St001298The number of repeated entries in the Lehmer code of a permutation. St000146The Andrews-Garvan crank of a partition. St000837The number of ascents of distance 2 of a permutation. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St000533The minimum of the number of parts and the size of the first part of an integer partition. St001090The number of pop-stack-sorts needed to sort a permutation. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001875The number of simple modules with projective dimension at most 1. St000890The number of nonzero entries in an alternating sign matrix. St001925The minimal number of zeros in a row of an alternating sign matrix. St000093The cardinality of a maximal independent set of vertices of a graph. St000246The number of non-inversions of a permutation. St000883The number of longest increasing subsequences of a permutation. St000050The depth or height of a binary tree. St001645The pebbling number of a connected graph. St000336The leg major index of a standard tableau. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000163The size of the orbit of the set partition under rotation. St001340The cardinality of a minimal non-edge isolating set of a graph. St000273The domination number of a graph. St000662The staircase size of the code of a permutation. 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. St001268The size of the largest ordinal summand in the poset. St001779The order of promotion on the set of linear extensions of a poset. St000656The number of cuts of a poset. St000167The number of leaves of an ordered tree. St000449The number of pairs of vertices of a graph with distance 4. St001725The harmonious chromatic number 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. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001280The number of parts of an integer partition that are at least two. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000454The largest eigenvalue of a graph if it is integral. St000308The height of the tree associated to a permutation. St000819The propagating number of a perfect matching. St000957The number of Bruhat lower covers of a permutation. St000783The side length of the largest staircase partition fitting into a partition. 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. 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. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St000051The size of the left subtree of a binary tree. 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. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001391The disjunction number of a graph. St001480The number of simple summands of the module J^2/J^3. St001649The length of a longest trail in a graph. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St000031The number of cycles in the cycle decomposition of a permutation. St000083The number of left oriented leafs of a binary tree except the first one. St000225Difference between largest and smallest parts in a partition. St000229Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition. St000299The number of nonisomorphic vertex-induced subtrees. St000309The number of vertices with even degree. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000354The number of recoils of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000703The number of deficiencies of a permutation. St000733The row containing the largest entry of a standard tableau. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000829The Ulam distance of a permutation to the identity permutation. 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. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001180Number of indecomposable injective modules with projective dimension at most 1. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001489The maximum of the number of descents and the number of inverse descents. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St000451The length of the longest pattern of the form k 1 2. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001182Number of indecomposable injective modules with codominant dimension at least two in 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. St000015The number of peaks of a Dyck path. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. 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. St000080The rank of the poset. St000133The "bounce" of a permutation. 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. St000306The bounce count of a Dyck path. St000325The width of the tree associated to a permutation. St000331The number of upper interactions of a Dyck path. St000443The number of long tunnels of a Dyck path. St000470The number of runs in a permutation. St000482The (zero)-forcing number of a graph. St000542The number of left-to-right-minima of a permutation. St000619The number of cyclic descents of a permutation. St000638The number of up-down runs of a permutation. St000652The maximal difference between successive positions of a permutation. St000809The reduced reflection length of the permutation. St000831The number of indices that are either descents or recoils. St000840The number of closers smaller than the largest opener in a perfect matching. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St000961The shifted major index 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. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. 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. St001187The number of simple modules with grade at least one 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. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. 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. 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. St001345The Hamming dimension of a graph. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001516The number of cyclic bonds 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. St001963The tree-depth of a graph. St000021The number of descents 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. St000168The number of internal nodes of an ordered tree. St000226The convexity of a permutation. St000235The number of indices that are not cyclical small weak excedances. St000238The number of indices that are not small weak excedances. St000240The number of indices that are not small excedances. St000242The number of indices that are not cyclical small weak excedances. St000471The sum of the ascent tops of a permutation. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle 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. St000547The number of even non-empty partial sums of an integer partition. St000617The number of global maxima of a Dyck path. St000632The jump number of the poset. 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. St000795The mad of a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000906The length of the shortest maximal chain in a poset. St000924The number of topologically connected components of a perfect matching. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001061The number of indices that are both descents and recoils of a permutation. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. 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. 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. 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. 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. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001252Half the sum of the even parts of a partition. 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. St001310The number of induced diamond graphs in a graph. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001405The number of bonds in a permutation. St001519The pinnacle sum of a permutation. St001530The depth of a Dyck path. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001717The largest size of an interval in a poset. St001742The difference of the maximal and the minimal degree in a graph. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001883The mutual visibility number of a graph. St000068The number of minimal elements in a poset. St000071The number of maximal chains in a poset. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000312The number of leaves in a graph. St000456The monochromatic index of a connected graph. St000527The width of the poset. St000637The length of the longest cycle in a graph. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000836The number of descents of distance 2 of a permutation. 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 $c_{n−1}$. St001019Sum of the projective dimensions of the simple modules 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. St001233The number of indecomposable 2-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. St001350Half of the Albertson index of a graph. St001356The number of vertices in prime modules of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001468The smallest fixpoint of a permutation. St001664The number of non-isomorphic subposets of a poset. St001782The order of rowmotion on the set of order ideals of a poset. St000915The Ore degree of a graph. St001138The number of indecomposable modules with projective dimension or injective dimension at most one in the corresponding Nakayama algebra. St001812The biclique partition number of a graph. St000272The treewidth of a graph. St000536The pathwidth of a graph. St000778The metric dimension of a graph. St001029The size of the core of a graph. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001116The game chromatic number of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001644The dimension of a graph. St001136The largest label with larger sister in the leaf labelled binary unordered tree associated with the perfect matching. St000287The number of connected components of a graph. St001330The hat guessing number of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001828The Euler characteristic of a graph. St001432The order dimension of the 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. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St000741The Colin de Verdière graph invariant. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001962The proper pathwidth of a graph. St000286The number of connected components of the complement of a graph. St000822The Hadwiger number of the graph. St001302The number of minimally dominating sets of vertices of a graph. St001316The domatic number of a graph. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001458The rank of the adjacency matrix of a graph. St001498The normalised height of a Nakayama algebra with magnitude 1. St000744The length of the path to the largest entry in a standard Young tableau. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001118The acyclic chromatic index of a graph. St001214The aft of an integer partition. St000473The number of parts of a partition that are strictly bigger than the number of ones. St001397Number of pairs of incomparable elements in a finite poset. St000549The number of odd partial sums of an integer partition. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. 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. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. 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 $eA$. 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. St000797The stat`` of a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001511The minimal number of transpositions needed to sort a permutation in either direction. St001557The number of inversions of the second entry of a permutation. St001668The number of points of the poset minus the width of the poset. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001520The number of strict 3-descents. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St000039The number of crossings of a permutation. St000095The number of triangles of a graph. St000222The number of alignments in the permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000538The number of even inversions of a permutation. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001439The number of even weak deficiencies and of odd weak exceedences. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001637The number of (upper) dissectors of a poset. St001727The number of invisible inversions of a permutation. St001927Sparre Andersen's number of positives of a signed permutation. St000004The major index of a permutation. St000005The bounce statistic of a Dyck path. St000154The sum of the descent bottoms of a permutation. St000156The Denert 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. St000358The number of occurrences of the pattern 31-2. St000450The number of edges minus the number of vertices plus 2 of a graph. St000726The normalized sum of the leaf labels of the increasing binary tree associated to a permutation. St000780The size of the orbit under rotation of a perfect matching. St000896The number of zeros on the main diagonal of an alternating sign matrix. St000988The orbit size of a permutation under Foata's bijection. 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. 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. St001428The number of B-inversions of a signed permutation. St001429The number of negative entries in a signed permutation. St001574The minimal number of edges to add or remove to make a graph regular. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001576The minimal number of edges to add or remove to make a graph vertex transitive. St001690The length of a longest path in a graph such that after removing the paths edges, every vertex of the path has distance two from some other vertex of the path. St001726The number of visible inversions of a permutation. St000064The number of one-box pattern of a permutation. St000231Sum of the maximal elements of the blocks of a set partition. St000868The aid statistic in the sense of Shareshian-Wachs. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001040The depth of the decreasing labelled binary unordered tree associated with the perfect matching. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001556The number of inversions of the third entry of a permutation. St001565The number of arithmetic progressions of length 2 in a permutation. St001948The number of augmented double ascents of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St001706The number of closed sets in a graph. St000691The number of changes of a binary word. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St001896The number of right descents of a signed permutations. St001817The number of flag weak exceedances of a signed permutation. St001892The flag excedance statistic of a signed permutation. St000455The second largest eigenvalue of a graph if it is integral. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001434The number of negative sum pairs of a signed permutation. St000834The number of right outer peaks of a permutation. St001845The number of join irreducibles minus the rank of a lattice. St000035The number of left outer peaks of a permutation. St000352The Elizalde-Pak rank of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000945The number of matchings in the dihedral orbit of a perfect matching. St001060The distinguishing index of a graph. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St000884The number of isolated descents of a permutation. St000044The number of vertices of the unicellular map given by a perfect matching. St000017The number of inversions of a standard tableau. St000389The number of runs of ones of odd length in a binary word. St000753The Grundy value for the game of Kayles on a binary word. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001424The number of distinct squares in a binary word. St001712The number of natural descents of a standard Young tableau. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St000135The number of lucky cars of the parking function. St001171The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001423The number of distinct cubes in a binary word. St001462The number of factors of a standard tableaux under concatenation. St001684The reduced word complexity of a permutation. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000820The number of compositions obtained by rotating the composition. St000292The number of ascents of a binary word. St001220The width of a permutation. St001517The length of a longest pair of twins in a permutation. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001667The maximal size of a pair of weak twins for a permutation. St001769The reflection length of a signed permutation. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001811The Castelnuovo-Mumford regularity of a permutation. St001821The sorting index of a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001863The number of weak excedances of a signed permutation. St001864The number of excedances of a signed permutation. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St001894The depth of a signed permutation. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St001926Sparre Andersen's position of the maximum of a signed permutation. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000291The number of descents of a binary word. St000693The modular (standard) major index of a standard tableau. 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. St001413Half the length of the longest even length palindromic prefix of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001427The number of descents of a signed permutation. St001485The modular major index of a binary word. St001524The degree of symmetry of a binary word. St001569The maximal modular displacement of a permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001697The shifted natural comajor index of a standard Young tableau. St001768The number of reduced words of a signed permutation. St001770The number of facets of a certain subword complex associated with the signed permutation. St001822The number of alignments of a signed permutation. St001823The Stasinski-Voll length of a signed permutation. St001848The atomic length of a signed permutation. St001855The number of signed permutations less than or equal to a signed permutation in left weak order. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001862The number of crossings of a signed permutation. St001866The nesting alignments of a signed permutation. St001935The number of ascents in a parking function. St000013The height of a Dyck path. St000297The number of leading ones in a binary word. St001115The number of even descents of a permutation. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001555The order of a signed permutation. St001867The number of alignments of type EN of a signed permutation. St000508Eigenvalues of the random-to-random operator acting on a simple module. St000735The last entry on the main diagonal of a standard tableau. 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. St001486The number of corners of the ribbon associated with an integer composition. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module.