St001110The 3-dynamic chromatic number of a graph. St001571The Cartan determinant of the integer partition. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001674The number of vertices of the largest induced star graph in the graph. St000171The degree of the graph. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St001117The game chromatic index of a graph. St001120The length of a longest path in a graph. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001649The length of a longest trail in a graph. St001814The number of partitions interlacing the given partition. St001826The maximal number of leaves on a vertex of a graph. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000005The bounce statistic of a Dyck path. St000010The length of the partition. St000013The height of a Dyck path. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000120The number of left tunnels of a Dyck path. St000160The multiplicity of the smallest part of a partition. St000172The Grundy number of a graph. St000335The difference of lower and upper interactions. St000346The number of coarsenings of a partition. St000378The diagonal inversion number of an integer partition. St000388The number of orbits of vertices of a graph under automorphisms. 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. St000519The largest length of a factor maximising the subword complexity. St000548The number of different non-empty partial sums of an integer partition. St000676The number of odd rises of a Dyck path. St000734The last entry in the first row of a standard tableau. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000822The Hadwiger number of the graph. St000922The minimal number such that all substrings of this length are unique. St000947The major index east count of a Dyck path. St000982The length of the longest constant subword. St001029The size of the core of a graph. St001116The game chromatic number of a graph. St001161The major index north count of a Dyck path. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. 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. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001330The hat guessing number of a graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001494The Alon-Tarsi number of a graph. St001498The normalised height of a Nakayama algebra with magnitude 1. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001660The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board. St001670The connected partition number of a graph. St001809The index of the step at the first peak of maximal height in a Dyck path. St001883The mutual visibility number of a graph. St001933The largest multiplicity of a part in an integer partition. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St001963The tree-depth of a graph. St000271The chromatic index of a graph. St000272The treewidth of a graph. St000377The dinv defect of an integer partition. St000439The position of the first down step of a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St000454The largest eigenvalue of a graph if it is integral. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St001091The number of parts in an integer partition whose next smaller part has the same size. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001358The largest degree of a regular subgraph of a graph. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001644The dimension of a graph. St001743The discrepancy of a graph. St001792The arboricity of a graph. St001962The proper pathwidth of a graph. St000011The number of touch points (or returns) of a Dyck path. St000012The area of a Dyck path. St000015The number of peaks of a Dyck path. St000093The cardinality of a maximal independent set of vertices of a graph. St000144The pyramid weight of the Dyck path. St000288The number of ones in a binary word. St000290The major index of a binary word. St000297The number of leading ones in a binary word. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000381The largest part of an integer composition. St000392The length of the longest run of ones in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000443The number of long tunnels of a Dyck path. St000617The number of global maxima of a Dyck path. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000678The number of up steps after the last double rise of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. 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. 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. St000753The Grundy value for the game of Kayles on a binary word. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000808The number of up steps of the associated bargraph. St000877The depth of the binary word interpreted as a path. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000983The length of the longest alternating subword. St000984The number of boxes below precisely one peak. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. 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. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. 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. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module 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. 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: 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. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. 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. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001313The number of Dyck paths above the lattice path given by a binary word. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001372The length of a longest cyclic run of ones of a binary word. St001415The length of the longest palindromic prefix of a binary word. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001480The number of simple summands of the module J^2/J^3. St001481The minimal height of a peak of a Dyck path. St001485The modular major index of a binary word. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. 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. St001733The number of weak left to right maxima of a Dyck path. St001775The degree of the minimal polynomial of the largest eigenvalue of a graph. St001955The number of natural descents for set-valued two row standard Young tableaux. St000024The number of double up and double down steps of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000052The number of valleys of a Dyck path not on the x-axis. St000053The number of valleys of the Dyck path. St000157The number of descents of a standard tableau. St000306The bounce count of a Dyck path. 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. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000420The number of Dyck paths that are weakly above a Dyck path. St000674The number of hills of a Dyck path. St000682The Grundy value of Welter's game on a binary word. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000932The number of occurrences of the pattern UDU in a Dyck path. 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 $c_{n-1}$. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. 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. St001012Number of simple modules with projective dimension at most 2 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. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. 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. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. 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. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001172The number of 1-rises at odd height of a Dyck path. 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. St001188The number of simple modules $S$ with grade $\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra $A$ corresponding to the Dyck path. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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 $eA$. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. 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. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of 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. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. 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. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001349The number of different graphs obtained from the given graph by removing an edge. 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. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001777The number of weak descents in an integer composition. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001808The box weight or horizontal decoration of a Dyck path. St001812The biclique partition number of a graph. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St000668The least common multiple of the parts of the partition. St001592The maximal number of simple paths between any two different vertices of a graph. St001742The difference of the maximal and the minimal degree in a graph. St000100The number of linear extensions of a poset. St000455The second largest eigenvalue of a graph if it is integral. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St000770The major index of an integer partition when read from bottom to top. St000937The number of positive values of the symmetric group character corresponding to the partition. St001118The acyclic chromatic index of a graph. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000939The number of characters of the symmetric group whose value on the partition is positive. St000993The multiplicity of the largest part of an integer partition. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St000086The number of subgraphs. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000269The number of acyclic orientations of a graph. St000270The number of forests contained in a graph. St000286The number of connected components of the complement of a graph. St000343The number of spanning subgraphs of a graph. St000363The number of minimal vertex covers of a graph. St000452The number of distinct eigenvalues of a graph. St000468The Hosoya index of a graph. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000722The number of different neighbourhoods in a graph. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000972The composition number of a graph. St001109The number of proper colourings of a graph with as few colours as possible. St001128The exponens consonantiae of a partition. St001261The Castelnuovo-Mumford regularity of a graph. St001316The domatic number of a graph. St001389The number of partitions of the same length below the given integer partition. St001474The evaluation of the Tutte polynomial of the graph at (x,y) equal to (2,-1). St001527The cyclic permutation representation number of an integer partition. St001725The harmonious chromatic number of a graph. St001758The number of orbits of promotion on a graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000263The Szeged index of a graph. St000265The Wiener index of a graph. St000274The number of perfect matchings of a graph. St000310The minimal degree of a vertex of a graph. St000361The second Zagreb index of a graph. St000387The matching number of a graph. St000535The rank-width of a graph. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000934The 2-degree of an integer partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001056The Grundy value for the game of deleting vertices of a graph until it has no edges. St001071The beta invariant of the graph. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. 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. St001119The length of a shortest maximal path in a graph. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001271The competition number of a graph. St001280The number of parts of an integer partition that are at least two. St001333The cardinality of a minimal edge-isolating set of a graph. St001341The number of edges in the center of a graph. St001354The number of series nodes in the modular decomposition of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001362The normalized Knill dimension of a graph. St001393The induced matching number of a graph. St001395The number of strictly unfriendly partitions of a graph. St001479The number of bridges of a graph. St001512The minimum rank of a graph. St001541The Gini index of an integer partition. St001587Half of the largest even part of an integer partition. St001657The number of twos in an integer partition. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001783The number of odd automorphisms of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001869The maximum cut size of a graph. St000675The number of centered multitunnels of a Dyck path. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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 $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St000273The domination number of a graph. St000287The number of connected components of a graph. St000438The position of the last up step in a Dyck path. St000482The (zero)-forcing number of a graph. St000544The cop number of a graph. St000553The number of blocks of a graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000775The multiplicity of the largest eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000806The semiperimeter of the associated bargraph. St000874The position of the last double rise in a Dyck path. St000916The packing number of a graph. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001286The annihilation number of a graph. St001322The size of a minimal independent dominating set in 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. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001642The Prague dimension of a graph. St001765The number of connected components of the friends and strangers graph. St001828The Euler characteristic of a graph. St001829The common independence number of a graph. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000508Eigenvalues of the random-to-random operator acting on a simple module. St000658The number of rises of length 2 of a Dyck path. St000661The number of rises of length 3 of a Dyck path. St000931The number of occurrences of the pattern UUU in a Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001141The number of occurrences of hills of size 3 in a Dyck path. St001176The size of a partition minus its first part. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001799The number of proper separations of a graph. St001961The sum of the greatest common divisors of all pairs of parts. St001645The pebbling number of a connected graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000450The number of edges minus the number of vertices plus 2 of a graph. St001574The minimal number of edges to add or remove to make a graph regular. St001576The minimal number of edges to add or remove to make a graph vertex transitive. St000474Dyson's crank of a partition. St000997The even-odd crank of an integer partition. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000781The number of proper colouring schemes of a Ferrers diagram. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001568The smallest positive integer that does not appear twice in the partition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. 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. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000929The constant term of the character polynomial of an integer partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a 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. St001383The BG-rank of an integer partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St000706The product of the factorials of the multiplicities of an integer partition. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001564The value of the forgotten symmetric functions when all variables set to 1. St001563The value of the power-sum symmetric function evaluated at 1. St001593This is the number of standard Young tableaux of the given shifted shape. St000928The sum of the coefficients of the character polynomial of an integer partition. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001624The breadth of a lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St000302The determinant of the distance matrix of a connected graph. St000467The hyper-Wiener index of a connected graph. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000264The girth of a graph, which is not a tree. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000456The monochromatic index of a connected graph. St000524The number of posets with the same order polynomial. St000525The number of posets with the same zeta polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000633The size of the automorphism group of a poset. St000635The number of strictly order preserving maps of a poset into itself. St000640The rank of the largest boolean interval in a poset. St000910The number of maximal chains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001890The maximum magnitude of the Möbius function of a poset. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000815The number of semistandard Young tableaux of partition weight of given shape. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St000850The number of 1/2-balanced pairs in a poset. St000933The number of multipartitions of sizes given by an integer partition. St001060The distinguishing index of a graph. St001095The number of non-isomorphic posets with precisely one further covering relation. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000478Another weight of a partition according to Alladi. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St001281The normalized isoperimetric number of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001545The second Elser number of a connected graph. St000464The Schultz index of a connected graph. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St000567The sum of the products of all pairs of parts. St000699The toughness times the least common multiple of 1,. St001099The 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 leaf labelled binary trees. St001100The 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 leaf labelled trees.