St000542The number of left-to-right-minima of a permutation. St000668The least common multiple of the parts of the partition. St000676The number of odd rises of a Dyck path. St000702The number of weak deficiencies of a permutation. St000733The row containing the largest entry of a standard tableau. 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. St000942The number of critical left to right maxima of the parking functions. St000991The number of right-to-left minima of a permutation. St001068Number of torsionless simple modules in 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. St000053The number of valleys of the Dyck path. St000157The number of descents of a standard tableau. St000160The multiplicity of the smallest part of a partition. St000216The absolute length of a permutation. 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. St000346The number of coarsenings of a partition. St000519The largest length of a factor maximising the subword complexity. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000548The number of different non-empty partial sums of an integer partition. St000617The number of global maxima of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000809The reduced reflection length of the 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. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001387Number of standard Young tableaux of the skew shape tracing the border of the given 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. 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. St001933The largest multiplicity of a part in an integer partition. St000052The number of valleys of a Dyck path not on the x-axis. St000118The number of occurrences of the contiguous pattern [.,[.,[.,.]]] in a binary tree. St000377The dinv defect of an integer partition. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St001091The number of parts in an integer partition whose next smaller part has the same size. St001172The number of 1-rises at odd height of a Dyck path. St001176The size of a partition minus its first part. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St000006The dinv of a Dyck path. St000011The number of touch points (or returns) of a Dyck path. St000025The number of initial rises of a Dyck path. St000058The order of a permutation. St000061The number of nodes on the left branch of a binary tree. St000062The length of the longest increasing subsequence of the permutation. St000068The number of minimal elements in a poset. St000069The number of maximal elements of a poset. St000084The number of subtrees. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000133The "bounce" of a permutation. St000164The number of short pairs. St000167The number of leaves of an ordered tree. St000172The Grundy number of a graph. St000213The number of weak exceedances (also weak excedences) of a permutation. St000239The number of small weak excedances. St000273The domination number of a graph. St000291The number of descents of a binary word. St000294The number of distinct factors of a binary word. St000308The height of the tree associated to a permutation. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000325The width of the tree associated to a permutation. St000328The maximum number of child nodes in a tree. St000339The maf index of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000390The number of runs of ones in a binary word. St000392The length of the longest run of ones in a binary word. St000393The number of strictly increasing runs in a binary word. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000439The position of the first down step of a Dyck path. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000446The disorder of a permutation. St000470The number of runs in a permutation. St000482The (zero)-forcing number of a graph. St000485The length of the longest cycle of a permutation. St000507The number of ascents of a standard tableau. St000518The number of distinct subsequences in a binary word. St000653The last descent of a permutation. St000673The number of non-fixed points of a permutation. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000703The number of deficiencies of a permutation. 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. 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. St000883The number of longest increasing subsequences of a permutation. St000906The length of the shortest maximal chain in a poset. St000912The number of maximal antichains in a poset. St000916The packing number of a graph. St000925The number of topologically connected components of a set partition. St000982The length of the longest constant subword. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001029The size of the core of a graph. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001058The breadth of the ordered tree. St001116The game chromatic number of a graph. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001161The major index north count of a Dyck path. 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. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. 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: 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. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. 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. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001288The number of primes obtained by multiplying preimage and image of a permutation and adding one. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St001372The length of a longest cyclic run of ones of a binary word. St001389The number of partitions of the same length below the given integer partition. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001429The number of negative entries in a signed permutation. St001430The number of positive entries in a signed permutation. St001437The flex of a binary word. St001461The number of topologically connected components of the chord diagram of a permutation. St001462The number of factors of a standard tableaux under concatenation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001480The number of simple summands of the module J^2/J^3. St001494The Alon-Tarsi number of a graph. St001497The position of the largest weak excedence of a permutation. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001530The depth of a Dyck path. St001566The length of the longest arithmetic progression in a permutation. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001670The connected partition number of a graph. St001769The reflection length of a signed permutation. St001814The number of partitions interlacing the given partition. St001829The common independence number of a graph. St001963The tree-depth of a graph. St000021The number of descents of a permutation. St000024The number of double up and double down steps of a Dyck path. St000026The position of the first return of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000047The number of standard immaculate tableaux of a given shape. St000050The depth or height of a binary tree. St000063The number of linear extensions of a certain poset defined for an integer partition. St000083The number of left oriented leafs of a binary tree except the first one. St000108The number of partitions contained in the given partition. St000120The number of left tunnels of a Dyck path. St000144The pyramid weight of the Dyck path. St000155The number of exceedances (also excedences) of a permutation. St000159The number of distinct parts of the integer partition. 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. St000211The rank of the set partition. St000245The number of ascents of a permutation. St000272The treewidth of a graph. St000290The major index of a binary word. St000292The number of ascents of a binary word. St000296The length of the symmetric border of a binary word. St000297The number of leading ones in a binary word. St000306The bounce count of a Dyck path. St000316The number of non-left-to-right-maxima of a permutation. St000321The number of integer partitions of n that are dominated by an integer partition. St000331The number of upper interactions of a Dyck path. St000335The difference of lower and upper interactions. St000340The number of non-final maximal constant sub-paths of length greater than one. St000345The number of refinements of a partition. St000354The number of recoils of a permutation. St000362The size of a minimal vertex cover of a graph. St000532The total number of rook placements on a Ferrers board. St000536The pathwidth of a graph. St000546The number of global descents of a permutation. St000619The number of cyclic descents of a permutation. St000626The minimal period of a binary word. St000627The exponent of a binary word. St000651The maximal size of a rise in a permutation. St000652The maximal difference between successive positions of a permutation. St000667The greatest common divisor of the parts of the partition. St000672The number of minimal elements in Bruhat order not less than the permutation. St000710The number of big deficiencies of a permutation. St000729The minimal arc length of a set partition. St000730The maximal arc length of a set partition. 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. St000806The semiperimeter of the associated bargraph. St000831The number of indices that are either descents or recoils. St000863The length of the first row of the shifted shape of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000922The minimal number such that all substrings of this length are unique. St000935The number of ordered refinements of an integer partition. St000946The sum of the skew hook positions in a Dyck path. St000989The number of final rises of a permutation. St000990The first ascent of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. 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. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of 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. St001050The number of terminal closers of a set partition. St001061The number of indices that are both descents and recoils of a permutation. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001090The number of pop-stack-sorts needed to sort a permutation. St001152The number of pairs with even minimum in a perfect matching. 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. St001180Number of indecomposable injective modules with projective dimension at most 1. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. 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 $eA$. St001199The dominant 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 $eA$. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001233The number of indecomposable 2-dimensional modules with projective dimension one. 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. St001277The degeneracy of a graph. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. 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. St001358The largest degree of a regular subgraph of a graph. St001400The total number of Littlewood-Richardson tableaux of given shape. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001481The minimal height of a peak of a Dyck path. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001485The modular major index of a binary word. St001489The maximum of the number of descents and the number of inverse descents. St001498The normalised height of a Nakayama algebra with magnitude 1. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001527The cyclic permutation representation number of an integer partition. St001554The number of distinct nonempty subtrees of a binary tree. St001571The Cartan determinant of the integer partition. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001712The number of natural descents of a standard Young tableau. St001726The number of visible inversions of a permutation. St001733The number of weak left to right maxima of a Dyck path. St001777The number of weak descents in an integer composition. St001786The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order. St001812The biclique partition number of a graph. St001872The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra. St001884The number of borders of a binary word. St001971The number of negative eigenvalues of the adjacency matrix of the graph. St000012The area of a Dyck path. St000039The number of crossings of a permutation. St000065The number of entries equal to -1 in an alternating sign matrix. St000148The number of odd parts of a partition. St000204The number of internal nodes of a binary tree. St000217The number of occurrences of the pattern 312 in a permutation. St000222The number of alignments in the permutation. St000223The number of nestings in the permutation. St000228The size of a partition. St000295The length of the border of a binary word. 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. St000369The dinv deficit of a Dyck path. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000376The bounce deficit of a Dyck path. St000384The maximal part of the shifted composition of an integer partition. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000459The hook length of the base cell of a partition. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000475The number of parts equal to 1 in a partition. St000491The number of inversions of a set partition. St000496The rcs statistic of a set partition. St000497The lcb statistic of a set partition. St000555The number of occurrences of the pattern {{1,3},{2}} in 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. St000582The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 3 is maximal, (1,3) are consecutive in a block. 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. St000600The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, (1,3) are consecutive in a block. St000602The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal. St000610The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal. 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. St000648The number of 2-excedences of a permutation. St000674The number of hills of a Dyck path. St000677The standardized bi-alternating inversion number of a permutation. St000711The number of big exceedences of a permutation. St000731The number of double exceedences of a permutation. St000766The number of inversions of an integer composition. St000784The maximum of the length and the largest part of the integer partition. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000867The sum of the hook lengths in the first row of an integer partition. 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. 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. 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. St001022Number of simple modules with projective dimension 3 in the Nakayama algebra corresponding to the Dyck path. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001087The number of occurrences of the vincular pattern |12-3 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. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St001127The sum of the squares of the parts of a partition. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001181Number of indecomposable injective modules with grade at least 3 in the corresponding Nakayama algebra. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. 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. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. 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. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001541The Gini index of an integer partition. St001565The number of arithmetic progressions of length 2 in a permutation. St001572The minimal number of edges to remove to make a graph bipartite. St001573The minimal number of edges to remove to make a graph triangle-free. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001781The interlacing number of a set partition. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001841The number of inversions of a set partition. St001843The Z-index of a set partition. St001939The number of parts that are equal to their multiplicity in the integer partition. St001960The number of descents of a permutation minus one if its first entry is not one. St000187The determinant of an alternating sign matrix. St000741The Colin de Verdière graph invariant. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001330The hat guessing 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. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. 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. St000933The number of multipartitions of sizes given by an integer partition. St000937The number of positive values of the symmetric group character corresponding to the 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. 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. St000928The sum of the coefficients of the character polynomial of an integer partition. St001645The pebbling number of a connected graph. St001060The distinguishing index of a graph. St001118The acyclic chromatic index of a graph. 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. 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. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000284The Plancherel distribution on integer partitions. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. 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. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001128The exponens consonantiae of a partition. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. 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. St000941The number of characters of the symmetric group whose value on the partition is even. St000984The number of boxes below precisely one peak. St001877Number of indecomposable injective modules with projective dimension 2. St000455The second largest eigenvalue of a graph if it is integral. St000907The number of maximal antichains of minimal length in a poset. St000264The girth of a graph, which is not a tree. St001722The number of minimal chains with small intervals between a binary word and the top element. St001875The number of simple modules with projective dimension at most 1. 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. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001360The number of covering relations in Young's lattice below a partition. St001378The product of the cohook lengths of the integer partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. 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. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001961The sum of the greatest common divisors of all pairs of parts. St000214The number of adjacencies of a permutation. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000454The largest eigenvalue of a graph if it is integral. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St001570The minimal number of edges to add to make a graph Hamiltonian. St001651The Frankl number of a lattice. St000758The length of the longest staircase fitting into an integer composition. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001857The number of edges in the reduced word graph of a signed permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000236The number of cyclical small weak excedances. St000241The number of cyclical small excedances. St000248The number of anti-singletons of a set partition. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St001114The number of odd descents of a permutation. St001151The number of blocks with odd minimum. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001713The difference of the first and last value in the first row of the Gelfand-Tsetlin pattern. St001928The number of non-overlapping descents in a permutation. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000456The monochromatic index of a connected graph. St001063Numbers of 3-torsionfree simple modules in the corresponding Nakayama algebra. St001344The neighbouring number of a permutation. St001926Sparre Andersen's position of the maximum of a signed permutation. St000122The number of occurrences of the contiguous pattern [.,[.,[[.,.],.]]] in a binary tree. St000130The number of occurrences of the contiguous pattern [.,[[.,.],[[.,.],.]]] in a binary tree. St000132The number of occurrences of the contiguous pattern [[.,.],[.,[[.,.],.]]] in a binary tree. St000252The number of nodes of degree 3 of a binary tree. St001130The number of two successive successions in a permutation. St001470The cyclic holeyness of a permutation. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St001545The second Elser number of a connected graph. St000464The Schultz index of a connected graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000782The indicator function of whether a given perfect matching is an L & P matching. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001816Eigenvalues of the top-to-random operator acting on a simple module. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000274The number of perfect matchings of a graph. St000310The minimal degree of a vertex of a graph. St000311The number of vertices of odd degree in a graph. St000315The number of isolated vertices of a graph. 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 $eA$. 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 $eA$. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001734The lettericity of a graph. St001783The number of odd automorphisms of a graph. 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. St000181The number of connected components of the Hasse diagram for the poset. St000286The number of connected components of the complement of a graph. St000287The number of connected components of a graph. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001117The game chromatic index of a graph. St001518The number of graphs with the same ordinary spectrum as the given graph. St001642The Prague dimension of a graph. St001890The maximum magnitude of the Möbius function of a poset. St000095The number of triangles of a graph. St000096The number of spanning trees of a graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. St000309The number of vertices with even degree. St000322The skewness of a graph. St000447The number of pairs of vertices of a graph with distance 3. St000449The number of pairs of vertices of a graph with distance 4. St001577The minimal number of edges to add or remove to make a graph a cograph. St001578The minimal number of edges to add or remove to make a graph a line graph. 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. St001827The number of two-component spanning forests of a graph. St001871The number of triconnected components of a graph. St001964The interval resolution global dimension of a poset.