St000356The number of occurrences of the pattern 13-2. St000358The number of occurrences of the pattern 31-2. St000362The size of a minimal vertex cover of a graph. St000454The largest eigenvalue of a graph if it is integral. St000463The number of admissible inversions of a permutation. St000536The pathwidth of a graph. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001091The number of parts in an integer partition whose next smaller part has the same size. St001120The length of a longest path in a graph. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama 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. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001644The dimension of a graph. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001812The biclique partition number of a graph. St001962The proper pathwidth of a graph. St001971The number of negative eigenvalues of the adjacency matrix of the graph. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000172The Grundy number of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000363The number of minimal vertex covers of a graph. St000388The number of orbits of vertices of a graph under automorphisms. St000453The number of distinct Laplacian eigenvalues of a graph. St000482The (zero)-forcing number of a 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. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000822The Hadwiger number of the graph. St001029The size of the core of a graph. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001116The game chromatic number of a graph. 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. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001330The hat guessing number of a graph. St001352The number of internal nodes in the modular decomposition of a graph. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001642The Prague dimension of a graph. St001670The connected partition number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001725The harmonious chromatic number of a graph. St001883The mutual visibility number of a graph. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St001963The tree-depth of a graph. St000013The height of a Dyck path. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000039The number of crossings of a permutation. St000065The number of entries equal to -1 in an alternating sign matrix. St000089The absolute variation of a composition. St000119The number of occurrences of the pattern 321 in a permutation. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000142The number of even parts of a partition. St000143The largest repeated part of a partition. St000157The number of descents of a standard tableau. St000217The number of occurrences of the pattern 312 in a permutation. St000223The number of nestings in the permutation. St000233The number of nestings of a set partition. St000316The number of non-left-to-right-maxima of a permutation. St000317The cycle descent number of a permutation. St000355The number of occurrences of the pattern 21-3. St000359The number of occurrences of the pattern 23-1. St000365The number of double ascents of a permutation. St000366The number of double descents of a permutation. St000367The number of simsun double descents of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000377The dinv defect of an integer partition. St000378The diagonal inversion number of an integer partition. St000496The rcs statistic of a set partition. St000647The number of big descents of a permutation. St000648The number of 2-excedences of a permutation. St000676The number of odd rises of a Dyck path. St000731The number of double exceedences of a permutation. St000766The number of inversions of an integer composition. St000877The depth of the binary word interpreted as a path. St000921The number of internal inversions of a binary word. St000931The number of occurrences of the pattern UUU in a Dyck path. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001083The number of boxed occurrences of 132 in a permutation. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001411The number of patterns 321 or 3412 in a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St001727The number of invisible inversions of a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St001843The Z-index of a set partition. St000047The number of standard immaculate tableaux of a given shape. St000093The cardinality of a maximal independent set of vertices of a graph. St000277The number of ribbon shaped standard tableaux. St000288The number of ones in a binary word. St000340The number of non-final maximal constant sub-paths of length greater than one. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000722The number of different neighbourhoods in a graph. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000733The row containing the largest entry of a standard tableau. St000778The metric dimension of a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000808The number of up steps of the associated bargraph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. 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. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001917The order of toric promotion on the set of labellings of a graph. St000312The number of leaves in a graph. St000636The hull number of a graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St000646The number of big ascents of a permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000619The number of cyclic descents of a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000491The number of inversions of a set partition. St000497The lcb statistic of a set partition. St000565The major index of a set partition. St000572The dimension exponent of a set partition. St000581The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 2 is maximal. St000585The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block. St000594The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) are consecutive in a block. St000605The number of occurrences of the pattern {{1},{2,3}} such that 3 is maximal, (2,3) are consecutive in a block. St000606The number of occurrences of the pattern {{1},{2,3}} such that 1,3 are maximal, (2,3) are consecutive in a block. St000613The number of occurrences of the pattern {{1,3},{2}} such that 2 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000614The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, 3 is maximal, (2,3) are consecutive in a block. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000732The number of double deficiencies of a permutation. St000801The number of occurrences of the vincular pattern |312 in a permutation. St001552The number of inversions between excedances and fixed points of a permutation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000225Difference between largest and smallest parts in a partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St001638The book thickness of a graph. St000148The number of odd parts of a partition. St000160The multiplicity of the smallest part of a partition. St000292The number of ascents of a binary word. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000475The number of parts equal to 1 in a partition. St000519The largest length of a factor maximising the subword complexity. St000548The number of different non-empty partial sums of an integer partition. St000864The number of circled entries of the shifted recording tableau of a permutation. St001280The number of parts of an integer partition that are at least two. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St000145The Dyson rank of a partition. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St000015The number of peaks of a Dyck path. St000296The length of the symmetric border of a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000443The number of long tunnels of a Dyck path. St000549The number of odd partial sums of an integer partition. St000681The Grundy value of Chomp on Ferrers diagrams. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000734The last entry in the first row of a standard tableau. St000885The number of critical steps in the Catalan decomposition of a binary word. St001007Number of simple modules with projective dimension 1 in 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. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001126Number of simple module that are 1-regular 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. 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. 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. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. 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. St001480The number of simple summands of the module J^2/J^3. St001549The number of restricted non-inversions between exceedances. St001933The largest multiplicity of a part in an integer partition. St000671The maximin edge-connectivity for choosing a subgraph. St000535The rank-width of a graph. St000537The cutwidth of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001743The discrepancy of a graph. St001792The arboricity of a graph. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000259The diameter of a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001645The pebbling number of a connected graph. St001117The game chromatic index of a graph. St001592The maximal number of simple paths between any two different vertices of a graph. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000177The number of free tiles in the pattern. St000178Number of free entries. St000442The maximal area to the right of an up step of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000744The length of the path to the largest entry in a standard Young tableau. St000946The sum of the skew hook positions in a Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St000702The number of weak deficiencies of a permutation. St001435The number of missing boxes in the first row. St001022Number of simple modules with projective dimension 3 in the Nakayama algebra corresponding to the Dyck path. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001578The minimal number of edges to add or remove to make a graph a line graph. St001964The interval resolution global dimension of a poset. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module 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. St001960The number of descents of a permutation minus one if its first entry is not one. St001570The minimal number of edges to add to make a graph Hamiltonian. St000456The monochromatic index of a connected graph. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St000741The Colin de Verdière graph invariant. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000937The number of positive values of the symmetric group character corresponding to the partition. St000993The multiplicity of the largest part of an integer partition. St001868The number of alignments of type NE of a signed permutation. St001845The number of join irreducibles minus the rank of a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St000137The Grundy value of an integer partition. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000404The number of occurrences of the pattern 3241 or of the pattern 4231 in a permutation. St000460The hook length of the last cell along the main diagonal of an integer partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001389The number of partitions of the same length below the given integer partition. St001527The cyclic permutation representation number of an integer partition. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000782The indicator function of whether a given perfect matching is an L & P matching. St001651The Frankl number of a lattice. St001621The number of atoms of a lattice. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000284The Plancherel distribution on integer partitions. St000618The number of self-evacuating tableaux of given shape. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000667The greatest common divisor of the parts of the partition. St000668The least common multiple of the parts of the partition. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000770The major index of an integer partition when read from bottom to top. St000781The number of proper colouring schemes of a Ferrers diagram. St000815The number of semistandard Young tableaux of partition weight of given shape. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000929The constant term of the character polynomial of an integer partition. St000933The number of multipartitions of sizes given by an integer partition. St000941The number of characters of the symmetric group whose value on the partition is even. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001128The exponens consonantiae of a partition. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001383The BG-rank of an integer partition. St001423The number of distinct cubes in a binary word. St001432The order dimension of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001520The number of strict 3-descents. St001525The number of symmetric hooks on the diagonal of a partition. St001564The value of the forgotten symmetric functions when all variables set to 1. St001571The Cartan determinant of the integer partition. St001593This is the number of standard Young tableaux of the given shifted shape. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001780The order of promotion on the set of standard tableaux of given shape. St001811The Castelnuovo-Mumford regularity of a permutation. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001948The number of augmented double ascents of a permutation. St001967The coefficient of the monomial corresponding to the integer partition in a certain power series. St001968The coefficient of the monomial corresponding to the integer partition in a certain power series. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000567The sum of the products of all pairs of parts. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000934The 2-degree of an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001568The smallest positive integer that does not appear twice in the partition. St001095The number of non-isomorphic posets with precisely one further covering relation. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001722The number of minimal chains with small intervals between a binary word and the top element. St000091The descent variation of a composition. St000260The radius of a connected graph. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000562The number of internal points of a set partition. St000706The product of the factorials of the multiplicities of an integer partition. St000709The number of occurrences of 14-2-3 or 14-3-2. St000872The number of very big descents of a permutation. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001130The number of two successive successions in a permutation. St001470The cyclic holeyness of a permutation. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001857The number of edges in the reduced word graph of a signed permutation. St001867The number of alignments of type EN of a signed permutation. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St000243The number of cyclic valleys and cyclic peaks of a permutation. St001344The neighbouring number of a permutation. St001413Half the length of the longest even length palindromic prefix of a binary word. St001896The number of right descents of a signed permutations. St000236The number of cyclical small weak excedances. St000241The number of cyclical small excedances. St000248The number of anti-singletons of a set partition. St000302The determinant of the distance matrix of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St000879The number of long braid edges in the graph of braid moves of a permutation. St001060The distinguishing index of a graph.