St000025The number of initial rises of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000035The number of left outer peaks of a permutation. St000053The number of valleys of the Dyck path. St000141The maximum drop size of a permutation. St000142The number of even parts of a partition. St000185The weighted size of a partition. St000214The number of adjacencies of a permutation. St000237The number of small exceedances. St000246The number of non-inversions of a permutation. St000260The radius of a connected graph. St000272The treewidth of a graph. St000306The bounce count of a Dyck path. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000340The number of non-final maximal constant sub-paths of length greater than one. St000352The Elizalde-Pak rank of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000409The number of pitchforks in a binary tree. St000441The number of successions of a permutation. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000535The rank-width of a graph. St000546The number of global descents of a permutation. St000547The number of even non-empty partial sums of an integer partition. St000651The maximal size of a rise in a permutation. St000662The staircase size of the code of a permutation. St000665The number of rafts of a permutation. St000670The reversal length of a permutation. St000692Babson and Steingrímsson's statistic of a permutation. St000703The number of deficiencies of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000884The number of isolated descents of a permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001090The number of pop-stack-sorts needed to sort a permutation. St001092The number of distinct even parts of a partition. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001161The major index north count of a Dyck path. St001176The size of a partition minus its first part. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001252Half the sum of the even parts of a partition. St001271The competition number of a graph. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St001277The degeneracy of a graph. St001280The number of parts of an integer partition that are at least two. St001335The cardinality of a minimal cycle-isolating set of a graph. St001358The largest degree of a regular subgraph of a graph. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001587Half of the largest even part of an integer partition. St001657The number of twos in an integer partition. St001743The discrepancy of a graph. St001759The Rajchgot index of a permutation. St001792The arboricity of a graph. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St001961The sum of the greatest common divisors of all pairs of parts. St000007The number of saliances of the permutation. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000013The height of a Dyck path. St000031The number of cycles in the cycle decomposition of a permutation. St000040The number of regions of the inversion arrangement of a permutation. St000054The first entry of the permutation. St000058The order of a permutation. St000093The cardinality of a maximal independent set of vertices of a graph. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000110The number of permutations less than or equal to a permutation in left weak order. St000147The largest part of an integer partition. St000203The number of external nodes of a binary tree. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000258The burning number of a graph. St000273The domination number of a graph. 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. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000397The Strahler number of a rooted tree. St000451The length of the longest pattern of the form k 1 2. St000507The number of ascents of a standard tableau. St000528The height of a poset. St000544The cop number of a graph. St000553The number of blocks of a graph. St000644The number of graphs with given frequency partition. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. 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. St000740The last entry of a permutation. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000808The number of up steps of the associated bargraph. St000814The sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to Schur symmetric functions. St000883The number of longest increasing subsequences of a permutation. St000891The number of distinct diagonal sums of a permutation matrix. St000912The number of maximal antichains in a poset. St000916The packing number of a graph. St000920The logarithmic height of a Dyck path. St000935The number of ordered refinements of an integer partition. St000971The smallest closer of a set partition. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001029The size of the core of a graph. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001109The number of proper colourings of a graph with as few colours as possible. 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: St001316The domatic number of a graph. St001322The size of a minimal independent dominating set in a graph. St001330The hat guessing number of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001389The number of partitions of the same length below the given integer partition. St001461The number of topologically connected components of the chord diagram of a permutation. St001462The number of factors of a standard tableaux under concatenation. St001463The number of distinct columns in the nullspace of a graph. St001471The magnitude of a Dyck path. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001717The largest size of an interval in a poset. St001733The number of weak left to right maxima of a Dyck path. St001809The index of the step at the first peak of maximal height in a Dyck path. St001829The common independence number of a graph. St000439The position of the first down step of 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 $c_{n-1}$. St001028Number of simple modules with injective dimension equal to the dominant dimension 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St000504The cardinality of the first block of a set partition. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000823The number of unsplittable factors of the set partition. St001075The minimal size of a block of a set partition. St000502The number of successions of a set partitions. St000326The position of the first one in a binary word after appending a 1 at the end. St000487The length of the shortest cycle of a permutation. St000501The size of the first part in the decomposition of a permutation. St000542The number of left-to-right-minima of a permutation. St000659The number of rises of length at least 2 of a Dyck path. St000667The greatest common divisor of the parts of the partition. St000729The minimal arc length of a set partition. St000781The number of proper colouring schemes of a Ferrers diagram. St000990The first ascent of a permutation. 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. St001052The length of the exterior of a permutation. St001162The minimum jump of a permutation. St001344The neighbouring number of a permutation. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001468The smallest fixpoint of a permutation. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St000210Minimum over maximum difference of elements in cycles. St000297The number of leading ones in a binary word. St000379The number of Hamiltonian cycles in a graph. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000575The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element and 2 a singleton. St000623The number of occurrences of the pattern 52341 in a permutation. St000629The defect of a binary word. St000699The toughness times the least common multiple of 1,. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St000842The breadth of a permutation. St000929The constant term of the character polynomial of an integer partition. St000961The shifted major index of a permutation. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. 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. St001141The number of occurrences of hills of size 3 in a Dyck path. St001371The length of the longest Yamanouchi prefix of a binary word. St000026The position of the first return of a Dyck path. St000036The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation. St000056The decomposition (or block) number of a permutation. St000092The number of outer peaks of a permutation. St000183The side length of the Durfee square of an integer partition. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000253The crossing number of a set partition. St000286The number of connected components of the complement of a graph. St000288The number of ones in a binary word. St000314The number of left-to-right-maxima of a permutation. St000389The number of runs of ones of odd length in a binary word. St000390The number of runs of ones in a binary word. St000391The sum of the positions of the ones in a binary word. St000392The length of the longest run of ones in a binary word. St000402Half the size of the symmetry class of a permutation. St000420The number of Dyck paths that are weakly above a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St000456The monochromatic index of a connected graph. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000505The biggest entry in the block containing the 1. St000529The number of permutations whose descent word is the given binary word. St000543The size of the conjugacy class of a binary word. 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. St000626The minimal period of a binary word. St000627The exponent of a binary word. St000628The balance of a binary word. St000630The length of the shortest palindromic decomposition of a binary word. St000640The rank of the largest boolean interval in a poset. St000655The length of the minimal rise of a Dyck path. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000701The protection number of a binary tree. St000735The last entry on the main diagonal of a standard tableau. St000753The Grundy value for the game of Kayles on a binary word. St000756The sum of the positions of the left to right maxima of a permutation. St000762The sum of the positions of the weak records of an integer composition. St000792The Grundy value for the game of ruler on a binary word. St000847The number of standard Young tableaux whose descent set is the binary word. St000877The depth of the binary word interpreted as a path. St000908The length of the shortest maximal antichain in a poset. St000913The number of ways to refine the partition into singletons. St000914The sum of the values of the Möbius function of a poset. St000919The number of maximal left branches of a binary tree. St000932The number of occurrences of the pattern UDU in a Dyck path. St000946The sum of the skew hook positions in a Dyck path. St000947The major index east count of a Dyck path. St000983The length of the longest alternating subword. St000991The number of right-to-left minima of a permutation. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001063Numbers of 3-torsionfree simple modules in the corresponding Nakayama algebra. St001064Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy modules. 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. St001196The global dimension of $A$ minus the global dimension of $eAe$ for the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001256Number of simple reflexive modules that are 2-stable reflexive. St001267The length of the Lyndon factorization of the binary word. St001313The number of Dyck paths above the lattice path given by a binary word. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001372The length of a longest cyclic run of ones of a binary word. St001385The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition. 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. St001437The flex of a binary word. St001481The minimal height of a peak of a Dyck path. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001496The number of graphs with the same Laplacian spectrum as the given graph. St001498The normalised height of a Nakayama algebra with magnitude 1. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001568The smallest positive integer that does not appear twice in the partition. St001592The maximal number of simple paths between any two different vertices of a graph. St001613The binary logarithm of the size of the center of a lattice. St001665The number of pure excedances of a permutation. St001722The number of minimal chains with small intervals between a binary word and the top element. St001808The box weight or horizontal decoration of a Dyck path. St001838The number of nonempty primitive factors of a binary word. St001884The number of borders of a binary word. St000051The size of the left subtree of a binary tree. St000133The "bounce" of a permutation. St000149The number of cells of the partition whose leg is zero and arm is odd. 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. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000256The number of parts from which one can substract 2 and still get an integer partition. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000274The number of perfect matchings of a graph. St000279The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations. St000289The decimal representation of a binary word. St000290The major index of a binary word. St000291The number of descents of a binary word. St000292The number of ascents of a binary word. St000293The number of inversions of a binary word. St000295The length of the border of a binary word. St000296The length of the symmetric border of a binary word. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. St000310The minimal degree of a vertex of a graph. St000317The cycle descent number of a permutation. St000347The inversion sum of a binary word. St000348The non-inversion sum of a binary word. St000351The determinant of the adjacency matrix of a graph. St000353The number of inner valleys of a permutation. St000355The number of occurrences of the pattern 21-3. St000357The number of occurrences of the pattern 12-3. St000358The number of occurrences of the pattern 31-2. St000360The number of occurrences of the pattern 32-1. St000365The number of double ascents of a permutation. St000367The number of simsun double descents of a permutation. St000368The Altshuler-Steinberg determinant of a graph. St000369The dinv deficit of a Dyck path. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000376The bounce deficit of a Dyck path. St000406The number of occurrences of the pattern 3241 in a permutation. St000407The number of occurrences of the pattern 2143 in a permutation. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000427The number of occurrences of the pattern 123 or of the pattern 231 in a permutation. St000428The number of occurrences of the pattern 123 or of the pattern 213 in a permutation. St000430The number of occurrences of the pattern 123 or of the pattern 312 in a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000444The length of the maximal rise of a Dyck path. St000478Another weight of a partition according to Alladi. St000486The number of cycles of length at least 3 of a permutation. St000491The number of inversions of a set partition. St000497The lcb statistic of a set partition. St000508Eigenvalues of the random-to-random operator acting on a simple module. St000516The number of stretching pairs of a permutation. St000555The number of occurrences of the pattern {{1,3},{2}} in a set partition. St000559The number of occurrences of the pattern {{1,3},{2,4}} in a set partition. St000560The number of occurrences of the pattern {{1,2},{3,4}} in a set partition. St000561The number of occurrences of the pattern {{1,2,3}} in a set partition. St000562The number of internal points of a set partition. St000563The number of overlapping pairs of blocks of a set partition. St000565The major index of a set partition. St000572The dimension exponent of a set partition. St000573The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton and 2 a maximal element. St000578The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton. 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. St000588The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are minimal, 2 is maximal. 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. St000604The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 2 is maximal. 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. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000649The number of 3-excedences of a permutation. St000650The number of 3-rises of a permutation. St000661The number of rises of length 3 of a Dyck path. St000664The number of right ropes of a permutation. St000666The number of right tethers of a permutation. St000668The least common multiple of the parts of the partition. St000671The maximin edge-connectivity for choosing a subgraph. St000674The number of hills of a Dyck path. St000682The Grundy value of Welter's game on a binary word. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St000691The number of changes of a binary word. St000702The number of weak deficiencies of a permutation. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000709The number of occurrences of 14-2-3 or 14-3-2. St000711The number of big exceedences of a permutation. St000717The number of ordinal summands of a poset. St000726The normalized sum of the leaf labels of the increasing binary tree associated to a permutation. St000732The number of double deficiencies of a permutation. St000748The major index of the permutation obtained by flattening the set partition. St000750The number of occurrences of the pattern 4213 in a permutation. St000751The number of occurrences of either of the pattern 2143 or 2143 in a permutation. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000779The tier of a permutation. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. 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. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000906The length of the shortest maximal chain in a poset. St000921The number of internal inversions of a binary word. St000931The number of occurrences of the pattern UUU in a Dyck path. St000933The number of multipartitions of sizes given by an integer partition. St000962The 3-shifted major index of a permutation. St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St000981The length of the longest zigzag subpath. St001025Number of simple modules with projective dimension 4 in the Nakayama algebra corresponding to the Dyck path. St001059Number of occurrences of the patterns 41352,42351,51342,52341 in a permutation. St001095The number of non-isomorphic posets with precisely one further covering relation. St001119The length of a shortest maximal path in a graph. St001139The number of occurrences of hills of size 2 in a Dyck path. St001175The size of a partition minus the hook length of the base cell. St001193The dimension of $Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra $A$ such that $eA$ is a minimal faithful projective-injective module. St001281The normalized isoperimetric number of a graph. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001301The first Betti number of the order complex associated with the poset. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001357The maximal degree of a regular spanning subgraph of a graph. St001394The genus of a permutation. St001395The number of strictly unfriendly partitions of a graph. St001413Half the length of the longest even length palindromic prefix of a binary word. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001470The cyclic holeyness of a permutation. St001485The modular major index of a binary word. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001513The number of nested exceedences of a permutation. St001537The number of cyclic crossings of a permutation. St001549The number of restricted non-inversions between exceedances. St001550The number of inversions between exceedances where the greater exceedance is linked. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001552The number of inversions between excedances and fixed points of a permutation. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001712The number of natural descents of a standard Young tableau. St001715The number of non-records in a permutation. St001728The number of invisible descents of a permutation. St001730The number of times the path corresponding to a binary word crosses the base line. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001793The difference between the clique number and the chromatic number of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St000643The size of the largest orbit of antichains under Panyushev complementation. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St000061The number of nodes on the left branch of a binary tree. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000354The number of recoils of a permutation. St000472The sum of the ascent bottoms of a permutation. St000570The Edelman-Greene number of a permutation. St000654The first descent of a permutation. St000886The number of permutations with the same antidiagonal sums. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001159Number of simple modules with dominant dimension equal to the global dimension in the corresponding Nakayama algebra. 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. St001204Call 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. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. 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. St001859The number of factors of the Stanley symmetric function associated with a permutation. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000455The second largest eigenvalue of a graph if it is integral. St000461The rix statistic of a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000872The number of very big descents of a permutation. St000873The aix statistic of a permutation. St000963The 2-shifted major index of a permutation. St000989The number of final rises of a permutation. St001082The number of boxed occurrences of 123 in a permutation. St001130The number of two successive successions in a permutation. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. 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 $eA$. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001346The number of parking functions that give the same permutation. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St000918The 2-limited packing number of a graph. St001621The number of atoms of a lattice. St000219The number of occurrences of the pattern 231 in a permutation. St000264The girth of a graph, which is not a tree. St001571The Cartan determinant of the integer partition. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St000068The number of minimal elements in a poset. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001333The cardinality of a minimal edge-isolating set of a graph. St001393The induced matching number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001741The largest integer such that all patterns of this size are contained in the permutation. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000710The number of big deficiencies of a permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000065The number of entries equal to -1 in an alternating sign matrix. St001434The number of negative sum pairs of a signed permutation. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St000838The number of terminal right-hand endpoints when the vertices are written in order. 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. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001530The depth of a Dyck path. 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. St000298The order dimension or Dushnik-Miller dimension of a poset. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St001260The permanent of an alternating sign matrix. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001298The number of repeated entries in the Lehmer code of a permutation. St001737The number of descents of type 2 in a permutation. St000062The length of the longest increasing subsequence of the permutation. St000236The number of cyclical small weak excedances. St000239The number of small weak excedances. St000308The height of the tree associated to a permutation. St000004The major index of a permutation. St000005The bounce statistic of a Dyck path. St000006The dinv of a Dyck path. St000021The number of descents of a permutation. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000055The inversion sum of a permutation. St000080The rank of the poset. St000120The number of left tunnels of a Dyck path. St000154The sum of the descent bottoms of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000156The Denert index of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000209Maximum difference of elements in cycles. St000224The sorting index of a permutation. St000238The number of indices that are not small weak excedances. St000259The diameter of a connected graph. St000304The load of a permutation. St000305The inverse major index of a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000331The number of upper interactions of a Dyck path. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000339The maf index of a permutation. St000341The non-inversion sum of a permutation. St000446The disorder of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001079The minimal length of a factorization of a permutation using the permutations (12)(34). 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. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module 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. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension 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. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001274The number of indecomposable injective modules with projective dimension equal to two. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. 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. St001349The number of different graphs obtained from the given graph by removing an edge. St001354The number of series nodes in the modular decomposition of a graph. St001375The pancake length of a permutation. St001405The number of bonds in a permutation. St001412Number of minimal entries in the Bruhat order matrix of a permutation. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001489The maximum of the number of descents and the number of inverse descents. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001512The minimum rank of a graph. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001671Haglund's hag of a permutation. St001726The number of visible inversions of a permutation. St001729The number of visible descents of a permutation. St001760The number of prefix or suffix reversals needed to sort a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001801Half the number of preimage-image pairs of different parity in a permutation. St001874Lusztig's a-function for the symmetric group. St001928The number of non-overlapping descents in a permutation. St001958The degree of the polynomial interpolating the values of a permutation. St000015The number of peaks of a Dyck path. St000109The number of elements less than or equal to the given element in Bruhat order. St000213The number of weak exceedances (also weak excedences) of a permutation. St000240The number of indices that are not small excedances. St000287The number of connected components of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000325The width of the tree associated to a permutation. St000401The size of the symmetry class of a permutation. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000470The number of runs in a permutation. St000638The number of up-down runs of a permutation. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000822The Hadwiger number of the graph. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001093The detour number of a graph. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama 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. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001285The number of primes in the column sums of the two line notation of a permutation. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001299The product of all non-zero projective dimensions of simple modules of the corresponding Nakayama algebra. St001315The dissociation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001339The irredundance number of a graph. St001363The Euler characteristic of a graph according to Knill. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001497The position of the largest weak excedence of a permutation. St001652The length of a longest interval of consecutive numbers. St001661Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation. St001662The length of the longest factor of consecutive numbers in a permutation. St001674The number of vertices of the largest induced star graph in the 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. St000060The greater neighbor of the maximum. St000083The number of left oriented leafs of a binary tree except the first one. St000181The number of connected components of the Hasse diagram for the poset. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000216The absolute length of a permutation. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000494The number of inversions of distance at most 3 of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000530The number of permutations with the same descent word as the given permutation. St000539The number of odd inversions of a permutation. St000619The number of cyclic descents of a permutation. St000652The maximal difference between successive positions of a permutation. St000653The last descent of a permutation. St000694The number of affine bounded permutations that project to a given permutation. St000794The mak of a permutation. St000795The mad of a permutation. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000809The reduced reflection length of the permutation. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St000833The comajor index of a permutation. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St000988The orbit size of a permutation under Foata's bijection. St001061The number of indices that are both descents and recoils of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001081The number of minimal length factorizations of a permutation into star transpositions. St001114The number of odd descents of a permutation. St001208The number of connected components of the quiver of $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra $A$ of $K[x]/(x^n)$. St001220The width of a permutation. St001246The maximal difference between two consecutive entries of a permutation. St000064The number of one-box pattern of a permutation. St000226The convexity of a permutation. St000462The major index minus the number of excedences of a permutation. St000471The sum of the ascent tops of a permutation. St000485The length of the longest cycle of a permutation. St000538The number of even inversions of a permutation. St000624The normalized sum of the minimal distances to a greater element. St000646The number of big ascents of a permutation. St000673The number of non-fixed points of a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000824The sum of the number of descents and the number of recoils of a permutation. St000830The total displacement of a permutation. St000836The number of descents of distance 2 of a permutation. St000837The number of ascents of distance 2 of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000881The number of short braid edges in the graph of braid moves of a permutation. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. St001388The number of non-attacking neighbors of a permutation. St001429The number of negative entries in a signed permutation. St001516The number of cyclic bonds of a permutation. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001731The factorization defect of a permutation. St001771The number of occurrences of the signed pattern 1-2 in a signed permutation. St001856The number of edges in the reduced word graph of a permutation. St001870The number of positive entries followed by a negative entry in a signed permutation. St001895The oddness of a signed permutation. St000045The number of linear extensions of a binary tree. St000552The number of cut vertices of a graph. St001691The number of kings in a graph. St001948The number of augmented double ascents of a permutation. St001111The weak 2-dynamic chromatic number of a graph. St001520The number of strict 3-descents. St001557The number of inversions of the second entry of a permutation. St001570The minimal number of edges to add to make a graph Hamiltonian. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001556The number of inversions of the third entry of a permutation. St001811The Castelnuovo-Mumford regularity of a permutation. St001060The distinguishing index of a graph. St000862The number of parts of the shifted shape of a permutation. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001684The reduced word complexity of a permutation. St000033The number of permutations greater than or equal to the given permutation in (strong) Bruhat order. St000199The column of the unique '1' in the last row of the alternating sign matrix. St000200The row of the unique '1' in the last column of the alternating sign matrix. St000545The number of parabolic double cosets with minimal element being the given permutation. St001889The size of the connectivity set of a signed permutation. St000898The number of maximal entries in the last diagonal of the monotone triangle. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001569The maximal modular displacement of a permutation. St001668The number of points of the poset minus the width of the poset. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001890The maximum magnitude of the Möbius function of a poset. 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 $eA$. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001960The number of descents of a permutation minus one if its first entry is not one. St001875The number of simple modules with projective dimension at most 1. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.