St000069The number of maximal elements of a poset. St000093The cardinality of a maximal independent set of vertices of a graph. St000273The domination number of a graph. 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. St000544The cop number of a graph. St000759The smallest missing part in an integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000908The length of the shortest maximal antichain in a poset. St000916The packing number of a graph. St000971The smallest closer of a set partition. St001050The number of terminal closers of a set partition. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001463The number of distinct columns in the nullspace of a graph. St001691The number of kings in a graph. St001733The number of weak left to right maxima of a Dyck path. St001829The common independence number of a graph. St001176The size of a partition minus its first part. St001657The number of twos in an integer partition. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000063The number of linear extensions of a certain poset defined for an integer partition. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000108The number of partitions contained in the given partition. St000147The largest part of an integer partition. St000172The Grundy number of a graph. St000288The number of ones in a binary word. St000378The diagonal inversion number of an integer partition. St000532The total number of rook placements on a Ferrers board. St000700The protection number of an ordered tree. St000722The number of different neighbourhoods in a graph. St000733The row containing the largest entry of a standard tableau. St000738The first entry in the last row of a standard tableau. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. 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. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001029The size of the core of a graph. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001389The number of partitions of the same length below the given integer partition. St001400The total number of Littlewood-Richardson tableaux of given shape. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001670The connected partition number of a graph. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St000008The major index of the composition. St000012The area of a Dyck path. St000053The number of valleys of the Dyck path. 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. St000228The size of a partition. St000234The number of global ascents of a permutation. St000272The treewidth of a graph. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000362The size of a minimal vertex cover of a graph. St000384The maximal part of the shifted composition of an integer partition. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000459The hook length of the base cell of a partition. St000475The number of parts equal to 1 in a partition. St000519The largest length of a factor maximising the subword complexity. St000536The pathwidth of a graph. St000548The number of different non-empty partial sums of an integer partition. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000784The maximum of the length and the largest part of the integer partition. St000867The sum of the hook lengths in the first row of an integer partition. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001127The sum of the squares of the parts of a partition. St001777The number of weak descents in an integer composition. St001910The height of the middle non-run of a Dyck path. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000363The number of minimal vertex covers of a graph. St000678The number of up steps after the last double rise of a Dyck path. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St001826The maximal number of leaves on a vertex of a graph. St000287The number of connected components of a graph. St000504The cardinality of the first block of a set partition. St000553The number of blocks of a graph. St000823The number of unsplittable factors of the set partition. St000917The open packing number of a graph. St001672The restrained domination number of a graph. St000286The number of connected components of the complement of a graph. St000617The number of global maxima of a Dyck path. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000729The minimal arc length of a set partition. St000822The Hadwiger number of the graph. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001316The domatic number of a graph. St001963The tree-depth of a graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000502The number of successions of a set partitions. St000932The number of occurrences of the pattern UDU in a Dyck path. St000984The number of boxes below precisely one peak. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001812The biclique partition number of a graph. St001828The Euler characteristic of a graph. St001827The number of two-component spanning forests of a graph. St001479The number of bridges of a graph. St000914The sum of the values of the Möbius function of a poset. St000054The first entry of the permutation. St000993The multiplicity of the largest part of an integer partition. St001330The hat guessing number of a graph. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St000335The difference of lower and upper interactions. St000627The exponent of a binary word. St001481The minimal height of a peak of a Dyck path. St001884The number of borders of a binary word. St001933The largest multiplicity of a part in an integer partition. St001462The number of factors of a standard tableaux under concatenation. St000883The number of longest increasing subsequences of a permutation. St000546The number of global descents of a permutation. St000989The number of final rises of a permutation. St000501The size of the first part in the decomposition of a permutation. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St000237The number of small exceedances. St000454The largest eigenvalue of a graph if it is integral. St000542The number of left-to-right-minima of a permutation. St000740The last entry of a permutation. St000654The first descent of a permutation. St000990The first ascent 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. St001461The number of topologically connected components of the chord diagram of a permutation. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St000181The number of connected components of the Hasse diagram for the poset. St000007The number of saliances of the permutation. St000214The number of adjacencies of a permutation. St000441The number of successions of a permutation. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000203The number of external nodes of a binary tree. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St000031The number of cycles in the cycle decomposition of a permutation. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000838The number of terminal right-hand endpoints when the vertices are written in order. St000843The decomposition number of a perfect matching. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St000937The number of positive values of the symmetric group character corresponding to the partition. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000260The radius of a connected graph. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000667The greatest common divisor of the parts of the partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St001432The order dimension of the partition. St001527The cyclic permutation representation number of an integer partition. St001571The Cartan determinant of the integer partition. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001924The number of cells in an integer partition whose arm and leg length coincide. St000734The last entry in the first row of a standard tableau. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St000314The number of left-to-right-maxima of a permutation. St000991The number of right-to-left minima of a permutation. 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. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St000051The size of the left subtree of a binary tree. St000090The variation of a composition. St000258The burning number of a graph. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001274The number of indecomposable injective modules with projective dimension equal to two. St000015The number of peaks of a Dyck path. St000056The decomposition (or block) number of a permutation. St000084The number of subtrees. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000352The Elizalde-Pak rank of a permutation. St000460The hook length of the last cell along the main diagonal of an integer partition. St000618The number of self-evacuating tableaux of given shape. St000781The number of proper colouring schemes of a Ferrers diagram. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001118The acyclic chromatic index of a graph. 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. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. 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. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001360The number of covering relations in Young's lattice below a partition. St001498The normalised height of a Nakayama algebra with magnitude 1. St001780The order of promotion on the set of standard tableaux of given shape. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. 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. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000133The "bounce" of a permutation. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000331The number of upper interactions of a Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. 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. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001816Eigenvalues of the top-to-random operator acting on a simple module. St000061The number of nodes on the left branch of a binary tree. St001340The cardinality of a minimal non-edge isolating set of a graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St000918The 2-limited packing number of a graph. St001480The number of simple summands of the module J^2/J^3. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St000456The monochromatic index of a connected graph. St000731The number of double exceedences of a permutation. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001060The distinguishing index of a graph. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000939The number of characters of the symmetric group whose value on the partition is positive. St001128The exponens consonantiae of a partition. St001568The smallest positive integer that does not appear twice in the partition. St001133The smallest label in the subtree rooted at the sister of 1 in 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. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000782The indicator function of whether a given perfect matching is an L & P matching. St001877Number of indecomposable injective modules with projective dimension 2. 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. St000455The second largest eigenvalue of a graph if it is integral. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000338The number of pixed points of a permutation. St000060The greater neighbor of the maximum. 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. St000284The Plancherel distribution on integer partitions. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000681The Grundy value of Chomp on Ferrers diagrams. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000707The product of the factorials of the parts. St000770The major index of an integer partition when read from bottom to top. St000815The number of semistandard Young tableaux of partition weight of given shape. 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. St000241The number of cyclical small excedances. St000315The number of isolated vertices of a graph. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St001530The depth of a 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. St000756The sum of the positions of the left to right maxima of a permutation. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001615The number of join prime elements of a lattice. St000706The product of the factorials of the multiplicities of an integer partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001557The number of inversions of the second entry of a permutation. 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. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001414Half the length of the longest odd length palindromic prefix of a binary word.