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. St001733The number of weak left to right maxima of a Dyck path. St000439The position of the first down step of a Dyck path. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. 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. St000007The number of saliances of the permutation. St000026The position of the first return of a Dyck path. St000054The first entry of the permutation. St000056The decomposition (or block) number of a permutation. St000061The number of nodes on the left branch of a binary tree. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000068The number of minimal elements in a poset. St000069The number of maximal elements of a poset. St000084The number of subtrees. St000286The number of connected components of the complement of a graph. St000297The number of leading ones in a binary word. St000314The number of left-to-right-maxima of a permutation. St000326The position of the first one in a binary word after appending a 1 at the end. St000382The first part of an integer composition. St000383The last part of an integer composition. St000501The size of the first part in the decomposition of a permutation. St000504The cardinality of the first block of a set partition. St000542The number of left-to-right-minima of a permutation. St000617The number of global maxima of a Dyck path. St000675The number of centered multitunnels of a Dyck path. St000717The number of ordinal summands of a poset. St000740The last entry of a permutation. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000823The number of unsplittable factors of the set partition. St000838The number of terminal right-hand endpoints when the vertices are written in order. St000843The decomposition number of a perfect matching. St000883The number of longest increasing subsequences of a permutation. St000971The smallest closer of a set partition. St000991The number of right-to-left minima of a permutation. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001201The grade of the simple module $S_0$ in the special CNakayama 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. St001316The domatic number of a graph. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001461The number of topologically connected components of the chord diagram of a permutation. St001481The minimal height of a peak of a Dyck path. St000051The size of the left subtree of a binary tree. St000133The "bounce" of a permutation. St000214The number of adjacencies of a permutation. St000234The number of global ascents of a permutation. St000237The number of small exceedances. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000352The Elizalde-Pak rank 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. St000546The number of global descents of a permutation. St000658The number of rises of length 2 of a Dyck path. St000731The number of double exceedences of a permutation. St000738The first entry in the last row of a standard tableau. St000884The number of isolated descents of a permutation. St000932The number of occurrences of the pattern UDU in a Dyck path. St000989The number of final rises of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001114The number of odd descents of a permutation. St001139The number of occurrences of hills of size 2 in a Dyck path. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing 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. St001233The number of indecomposable 2-dimensional modules with projective dimension one. 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. St001274The number of indecomposable injective modules with projective dimension equal to two. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St000996The number of exclusive left-to-right maxima of a permutation. St001948The number of augmented double ascents of a permutation. St000193The row of the unique '1' in the first column of the alternating sign matrix. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of 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 $A$. St001238The number of simple modules S such that the Auslander-Reiten translate of S is isomorphic to the Nakayama functor applied to the second syzygy of S. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001516The number of cyclic bonds of a permutation. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St000338The number of pixed points of a permutation. St000665The number of rafts of a permutation. St000732The number of double deficiencies of a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St001115The number of even descents of a permutation. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive. 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. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001525The number of symmetric hooks on the diagonal of a partition. St001530The depth of a Dyck path. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St000460The hook length of the last cell along the main diagonal of an integer partition. St000531The leading coefficient of the rook polynomial of an integer partition. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001389The number of partitions of the same length below the given integer partition. 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. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000006The dinv of a Dyck path. St000010The length of the partition. St000013The height of a Dyck path. St000015The number of peaks of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000058The order of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000144The pyramid weight of the Dyck path. St000147The largest part of an integer partition. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000213The number of weak exceedances (also weak excedences) of a permutation. St000239The number of small weak excedances. St000308The height of the tree associated to a permutation. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000321The number of integer partitions of n that are dominated by an integer partition. St000345The number of refinements of a partition. St000346The number of coarsenings of a partition. St000378The diagonal inversion number of an integer partition. St000393The number of strictly increasing runs in a binary word. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000461The rix statistic of a permutation. St000494The number of inversions of distance at most 3 of a permutation. St000519The largest length of a factor maximising the subword complexity. St000548The number of different non-empty partial sums of an integer partition. St000638The number of up-down runs of a permutation. St000653The last descent of a permutation. St000655The length of the minimal 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. St000691The number of changes of a binary word. St000696The number of cycles in the breakpoint graph of a permutation. St000734The last entry in the first row of a standard tableau. St000784The maximum of the length and the largest part of the integer partition. St000847The number of standard Young tableaux whose descent set is the binary word. St000873The aix statistic of a permutation. St000885The number of critical steps in the Catalan decomposition of a binary word. St000886The number of permutations with the same antidiagonal sums. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St000922The minimal number such that all substrings of this length are unique. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000935The number of ordered refinements of an integer partition. St000968We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n−1}]$ by adding $c_0$ to $c_{n−1}$. St000982The length of the longest constant subword. St000983The length of the longest alternating subword. 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. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001032The number of horizontal steps in the bicoloured Motzkin path associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. 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. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. 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. St001267The length of the Lyndon factorization of the binary word. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. 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. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001439The number of even weak deficiencies and of odd weak exceedences. St001462The number of factors of a standard tableaux under concatenation. St001471The magnitude of a Dyck path. St001488The number of corners of a skew partition. St001500The global dimension of magnitude 1 Nakayama algebras. St001523The degree of symmetry of a Dyck path. St001660The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board. St001778The largest greatest common divisor of an element and its image in a permutation. St001806The upper middle entry of a permutation. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St000682The Grundy value of Welter's game on a binary word. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001904The length of the initial strictly increasing segment of a parking function. St001937The size of the center of a parking function. St001423The number of distinct cubes in a binary word. St001730The number of times the path corresponding to a binary word crosses the base line. St000454The largest eigenvalue of a graph if it is integral. St000993The multiplicity of the largest part of an integer partition. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. 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 $eA$. St000937The number of positive values of the symmetric group character corresponding to the partition. St001568The smallest positive integer that does not appear twice in the partition. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000668The least common multiple of the parts of the partition. St000681The Grundy value of Chomp on Ferrers diagrams. St000708The product of the parts of an integer partition. St000933The number of multipartitions of sizes given by an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000060The greater neighbor of the maximum. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000327The number of cover relations in a poset. St000385The number of vertices with out-degree 1 in a binary tree. St000402Half the size of the symmetry class of a permutation. St000418The number of Dyck paths that are weakly below a Dyck path. St000420The number of Dyck paths that are weakly above a Dyck path. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000489The number of cycles of a permutation of length at most 3. St000530The number of permutations with the same descent word as the given permutation. St000568The hook number of a binary tree. St000619The number of cyclic descents of a permutation. St000690The size of the conjugacy class of a permutation. St000702The number of weak deficiencies of a permutation. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000707The product of the factorials of the parts. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000729The minimal arc length of a set partition. St000744The length of the path to the largest entry in a standard Young tableau. 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. St000844The size of the largest block in the direct sum decomposition of a permutation. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000876The number of factors in the Catalan decomposition of a binary word. St000893The number of distinct diagonal sums of an alternating sign matrix. St000925The number of topologically connected components of a set partition. St001128The exponens consonantiae of a partition. St001246The maximal difference between two consecutive entries of a permutation. 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. St001437The flex of a binary word. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001531Number of partial orders contained in the poset determined by the Dyck path. St001607The number of coloured graphs 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. St001637The number of (upper) dissectors of a poset. St001808The box weight or horizontal decoration of a Dyck path. St001885The number of binary words with the same proper border set. St001959The product of the heights of the peaks 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 $eA$. 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 $eA$. St001498The normalised height of a Nakayama algebra with magnitude 1. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001933The largest multiplicity of a part in an integer partition. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000148The number of odd parts of a partition. St000160The multiplicity of the smallest part of a partition. St000179The product of the hook lengths of the integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000228The size of a partition. St000288The number of ones in a binary word. St000290The major index of a binary word. St000293The number of inversions of a binary word. St000296The length of the symmetric border of a binary word. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000392The length of the longest run of ones in a binary word. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000459The hook length of the base cell of a partition. St000475The number of parts equal to 1 in a partition. St000532The total number of rook placements on a Ferrers board. St000627The exponent of a binary word. St000644The number of graphs with given frequency partition. St000667The greatest common divisor of the parts of the partition. St000674The number of hills of a Dyck path. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000715The number of semistandard Young tableaux of given shape and entries at most 3. St000733The row containing the largest entry of a standard tableau. St000753The Grundy value for the game of Kayles on a binary word. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000792The Grundy value for the game of ruler on a binary word. St000867The sum of the hook lengths in the first row of an integer partition. St000878The number of ones minus the number of zeros of a binary word. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St000964Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra. St000965The sum of the dimension of Ext^i(D(A),A) for i=1,. 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 $c_{n-1}$. 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. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules 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. St001060The distinguishing index of a graph. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001127The sum of the squares of the parts of a partition. 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. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. 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. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001372The length of a longest cyclic run of ones of a binary word. St001387Number of standard Young tableaux of the skew shape tracing the border of the given partition. St001400The total number of Littlewood-Richardson tableaux of given shape. St001485The modular major index of a binary word. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. 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. St001501The 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. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001527The cyclic permutation representation number of an integer partition. St001571The Cartan determinant of the integer partition. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001732The number of peaks visible from the left. St001809The index of the step at the first peak of maximal height in a Dyck path. St001814The number of partitions interlacing the given partition. St001884The number of borders of a binary word. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000456The monochromatic index of a connected graph. St000706The product of the factorials of the multiplicities of an integer partition. St000762The sum of the positions of the weak records of an integer composition. St000817The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions. St000818The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. 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. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001967The coefficient of the monomial corresponding to the integer partition in a certain power series. St001968The coefficient of the monomial corresponding to the integer partition in a certain power series. St000741The Colin de Verdière graph invariant. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St001096The size of the overlap set of a permutation. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St001564The value of the forgotten symmetric functions when all variables set to 1. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St000260The radius of a connected graph. St000045The number of linear extensions of a binary tree. St000284The Plancherel distribution on integer partitions. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. 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. St001545The second Elser number of a connected graph. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001722The number of minimal chains with small intervals between a binary word and the top element. St000236The number of cyclical small weak excedances. St000241The number of cyclical small excedances. St000594The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) are consecutive in a block. St000613The number of occurrences of the pattern {{1,3},{2}} such that 2 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000663The number of right floats of a permutation. St001153The number of blocks with even minimum in a set partition. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001816Eigenvalues of the top-to-random operator acting on a simple module. St000090The variation of a composition. St000455The second largest eigenvalue of a graph if it is integral. St000567The sum of the products of all pairs of parts. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000929The constant term of the character polynomial of an integer partition. 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. 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. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St000137The Grundy value of an integer partition. St000264The girth of a graph, which is not a tree. St000421The number of Dyck paths that are weakly below a Dyck path, except for the path itself. St000442The maximal area to the right of an up step of a Dyck path. St000477The weight of a partition according to Alladi. St000478Another weight of a partition according to Alladi. St000509The diagonal index (content) of a partition. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000618The number of self-evacuating tableaux of given shape. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000659The number of rises of length at least 2 of a Dyck path. St000735The last entry on the main diagonal of a standard tableau. St000781The number of proper colouring schemes of a Ferrers diagram. St000782The indicator function of whether a given perfect matching is an L & P matching. St000806The semiperimeter of the associated bargraph. St000874The position of the last double rise in a Dyck path. St000934The 2-degree of an integer partition. St000946The sum of the skew hook positions in a Dyck path. St000976The sum of the positions of double up-steps of a Dyck path. St000984The number of boxes below precisely one peak. St000997The even-odd crank of an integer partition. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001118The acyclic chromatic index of a graph. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. 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. St001399The distinguishing number of a poset. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001432The order dimension of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001480The number of simple summands of the module J^2/J^3. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition. St001561The value of the elementary symmetric function evaluated at 1. St001562The value of the complete homogeneous symmetric function evaluated at 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. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. St001610The number of coloured endofunctions such that the multiplicities of colours are given by a partition. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001763The Hurwitz number of an integer partition. St001780The order of promotion on the set of standard tableaux of given shape. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001943The sum of the squares of the hook lengths of an integer partition. St001534The alternating sum of the coefficients of the Poincare polynomial of the poset cone.