St000503The maximal difference between two elements in a common block. 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. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St000653The last descent of a permutation. St000956The maximal displacement of a permutation. St001974The rank of the alternating sign matrix. St000672The number of minimal elements in Bruhat order not less than the permutation. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. 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. St001958The degree of the polynomial interpolating the values of a permutation. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000060The greater neighbor of the maximum. St000876The number of factors in the Catalan decomposition of a binary word. St001245The cyclic maximal difference between two consecutive entries of a permutation. St001622The number of join-irreducible elements of a lattice. St001246The maximal difference between two consecutive entries of a permutation. St000273The domination number of a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000916The packing number of a graph. St001286The annihilation number of a graph. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001829The common independence number of a graph. St000259The diameter of a connected graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St000288The number of ones in a binary word. St000528The height of a poset. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St000080The rank of the poset. St000906The length of the shortest maximal chain in a poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St001430The number of positive entries in a signed permutation. St000784The maximum of the length and the largest part of the integer partition. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001820The size of the image of the pop stack sorting operator. St000912The number of maximal antichains in a poset. St000680The Grundy value for Hackendot on posets. St000717The number of ordinal summands of a poset. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000019The cardinality of the support of a permutation. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001925The minimal number of zeros in a row of an alternating sign matrix. St001977The degree of an alternating sign matrix in the Hasse diagram of the corner sum lattice. St000924The number of topologically connected components of a perfect matching. 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. St001817The number of flag weak exceedances of a signed permutation. St001892The flag excedance statistic of a signed permutation. St000890The number of nonzero entries in an alternating sign matrix. St001434The number of negative sum pairs of a signed permutation. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St000519The largest length of a factor maximising the subword complexity. St000922The minimal number such that all substrings of this length are unique. St000703The number of deficiencies of a permutation. St001645The pebbling number of a connected graph. St001268The size of the largest ordinal summand in the poset. St000691The number of changes of a binary word. St000840The number of closers smaller than the largest opener in a perfect matching. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000018The number of inversions of a permutation. 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. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001725The harmonious chromatic number of a graph. St000031The number of cycles in the cycle decomposition of a permutation. St000352The Elizalde-Pak rank of a permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000374The number of exclusive right-to-left minima 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. St001082The number of boxed occurrences of 123 in a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St000141The maximum drop size of a permutation. St000054The first entry of the permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000740The last entry of a permutation. St001497The position of the largest weak excedence of a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St001978The codimension of the alternating sign matrix variety. St000197The number of entries equal to positive one in the alternating sign matrix. St000820The number of compositions obtained by rotating the composition. St001045The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching. St001132The number of leaves in the subtree whose sister has label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001480The number of simple summands of the module J^2/J^3. St000501The size of the first part in the decomposition of a permutation. St000673The number of non-fixed points of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001468The smallest fixpoint of a permutation. St000035The number of left outer peaks of a permutation. St000095The number of triangles of a graph. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000742The number of big ascents of a permutation after prepending zero. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000884The number of isolated descents of a permutation. St001214The aft of an integer partition. 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. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001777The number of weak descents in an integer composition. St001861The number of Bruhat lower covers of a permutation. St000029The depth of a permutation. St000051The size of the left subtree of a binary tree. St000067The inversion number of the alternating sign matrix. 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. St000203The number of external nodes of a binary tree. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. St000245The number of ascents of a permutation. St000316The number of non-left-to-right-maxima of a permutation. St000450The number of edges minus the number of vertices plus 2 of a graph. St000809The reduced reflection length of the permutation. St000834The number of right outer peaks of a permutation. St000957The number of Bruhat lower covers 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. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001429The number of negative entries in a signed permutation. St001437The flex of a binary word. St001555The order of a signed permutation. 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. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. St000189The number of elements in the poset. St000235The number of indices that are not cyclical small weak excedances. St000240The number of indices that are not small excedances. St000336The leg major index of a standard tableau. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St000026The position of the first return of a Dyck path. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001706The number of closed sets in a graph. St000744The length of the path to the largest entry in a standard Young tableau. St000044The number of vertices of the unicellular map given by a perfect matching. St000135The number of lucky cars of the parking function. St000327The number of cover relations in a poset. 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. St001984A recursive count of subwords of the form 01, 10 and 11. St000017The number of inversions of a standard tableau. St000896The number of zeros on the main diagonal of an alternating sign matrix. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St001413Half the length of the longest even length palindromic prefix 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. St001427The number of descents of a signed permutation. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001524The degree of symmetry of a binary word. St001855The number of signed permutations less than or equal to a signed permutation in left weak order. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000013The height of a Dyck path. St000292The number of ascents of a binary word. St000393The number of strictly increasing runs in a binary word. St001267The length of the Lyndon factorization of the binary word. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001424The number of distinct squares in a binary word. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001557The number of inversions of the second entry of a permutation. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001960The number of descents of a permutation minus one if its first entry is not one. St001927Sparre Andersen's number of positives of a signed permutation. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001684The reduced word complexity of a permutation. St001875The number of simple modules with projective dimension at most 1. St001926Sparre Andersen's position of the maximum of a signed permutation. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St001621The number of atoms of a lattice. St000028The number of stack-sorts needed to sort a permutation. St001096The size of the overlap set of a permutation. St001052The length of the exterior of a permutation. St000568The hook number of a binary tree. St000676The number of odd rises of a Dyck path. St000919The number of maximal left branches of a binary tree. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St000093The cardinality of a maximal independent set of vertices of a graph. St000527The width of the poset. St000845The maximal number of elements covered by an element in a poset. St000632The jump number of the poset. St000662The staircase size of the code of a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000007The number of saliances of the permutation. St000153The number of adjacent cycles of a permutation. St000237The number of small exceedances. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000490The intertwining number of a set partition. St000011The number of touch points (or returns) of a Dyck path. St000022The number of fixed points of a permutation. St000119The number of occurrences of the pattern 321 in a permutation. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000223The number of nestings in the permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000451The length of the longest pattern of the form k 1 2. St000502The number of successions of a set partitions. St000731The number of double exceedences of a permutation. St000052The number of valleys of a Dyck path not on the x-axis. St000356The number of occurrences of the pattern 13-2. St000647The number of big descents of a permutation. St001115The number of even descents of a permutation. St001769The reflection length of a signed permutation. St000024The number of double up and double down steps of a Dyck path. St000053The number of valleys of the Dyck path. St000271The chromatic index of a graph. St000272The treewidth of a graph. St000362The size of a minimal vertex cover of a graph. St000536The pathwidth of a graph. St000651The maximal size of a rise in a permutation. St000670The reversal length of a permutation. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001050The number of terminal closers of a set partition. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001358The largest degree of a regular subgraph of a graph. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001894The depth of a signed permutation. St001962The proper pathwidth of a graph. St001971The number of negative eigenvalues of the adjacency matrix of the graph. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000172The Grundy number of a graph. St000971The smallest closer of a set partition. 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. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001108The 2-dynamic chromatic number of a graph. St001116The game chromatic number of a graph. 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: St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001670The connected partition number of a graph. St001963The tree-depth of a graph. St001028Number of simple modules with injective dimension equal to the dominant dimension in 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. St000004The major index of a permutation. St000021The number of descents of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000105The number of blocks in the set partition. St000155The number of exceedances (also excedences) of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000211The rank of the set partition. St000213The number of weak exceedances (also weak excedences) of a permutation. St000251The number of nonsingleton blocks of a set partition. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. 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. St000354The number of recoils of a permutation. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000493The los statistic of a set partition. St000499The rcb statistic of a set partition. St000504The cardinality of the first block of a set partition. St000558The number of occurrences of the pattern {{1,2}} in a set partition. St000654The first descent of a permutation. St000702The number of weak deficiencies of a permutation. St000794The mak of a permutation. St000798The makl of a permutation. St000823The number of unsplittable factors of the set partition. St000829The Ulam distance of a permutation to the identity permutation. St000833The comajor index of a permutation. St000925The number of topologically connected components of a set partition. St000991The number of right-to-left minima of a permutation. St001062The maximal size of a block of a set partition. St001075The minimal size of a block of a set partition. St001220The width of a permutation. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001461The number of topologically connected components of the chord diagram of a permutation. St001489The maximum of the number of descents and the number of inverse descents. St001517The length of a longest pair of twins in a permutation. St001665The number of pure excedances of a permutation. St001667The maximal size of a pair of weak twins for a permutation. St001729The number of visible descents of a permutation. St001801Half the number of preimage-image pairs of different parity in a permutation. St001874Lusztig's a-function for the symmetric group. St000133The "bounce" of a permutation. St000168The number of internal nodes of an ordered tree. St000325The width of the tree associated to a permutation. St000338The number of pixed points of a permutation. St000358The number of occurrences of the pattern 31-2. St000470The number of runs in a permutation. St000609The number of occurrences of the pattern {{1},{2,3}} such that 1,2 are minimal. St000624The normalized sum of the minimal distances to a greater element. St000863The length of the first row of the shifted shape of a permutation. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000989The number of final rises of a permutation. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St000015The number of peaks of a Dyck path. St000030The sum of the descent differences of a permutations. St000056The decomposition (or block) number of a permutation. St000058The order of a permutation. St000075The orbit size of a standard tableau under promotion. St000083The number of left oriented leafs of a binary tree except the first one. St000092The number of outer peaks of a permutation. St000099The number of valleys of a permutation, including the boundary. St000156The Denert index of a permutation. St000171The degree of the graph. St000224The sorting index of a permutation. St000305The inverse major index of a permutation. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000387The matching number of a graph. St000442The maximal area to the right of an up step of a Dyck path. St000443The number of long tunnels of a Dyck path. St000446The disorder of a permutation. St000494The number of inversions of distance at most 3 of a permutation. St000542The number of left-to-right-minima of a permutation. St000552The number of cut vertices of a graph. St000619The number of cyclic descents of a permutation. St000652The maximal difference between successive positions of a permutation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000730The maximal arc length of a set partition. St000864The number of circled entries of the shifted recording tableau of a permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000990The first ascent of a permutation. St001112The 3-weak dynamic number of a graph. St001114The number of odd descents of a 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. 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 $eA$. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001566The length of the longest arithmetic progression in a permutation. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001642The Prague dimension of a graph. St001671Haglund's hag of a permutation. St001692The number of vertices with higher degree than the average degree in a graph. St001726The number of visible inversions of a permutation. St001733The number of weak left to right maxima of a Dyck path. St001737The number of descents of type 2 in a permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St001928The number of non-overlapping descents in a permutation. St000005The bounce statistic of a Dyck path. St000023The number of inner peaks of a permutation. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000039The number of crossings of a permutation. St000204The number of internal nodes of a binary tree. St000222The number of alignments in the permutation. St000234The number of global ascents of a permutation. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000317The cycle descent number of a permutation. St000331The number of upper interactions of a Dyck path. St000353The number of inner valleys of a permutation. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000491The number of inversions of a set partition. St000497The lcb statistic of a set partition. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000565The major index of a set partition. St000585The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block. St000586The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal. St000610The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal. St000614The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, 3 is maximal, (2,3) are consecutive in a block. St000636The hull number of a graph. St000638The number of up-down runs of a permutation. St000646The number of big ascents of a permutation. St000663The number of right floats of a permutation. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000710The number of big deficiencies of a permutation. St000711The number of big exceedences of a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000732The number of double deficiencies of a permutation. St000779The tier of a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St000872The number of very big descents of a permutation. St000932The number of occurrences of the pattern UDU in a Dyck path. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001078The minimal number of occurrences of (12) in a factorization of a permutation into transpositions (12) and cycles (1,. 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. St001120The length of a longest path in a graph. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001180Number of indecomposable injective modules with projective dimension at most 1. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001184Number of indecomposable injective modules with grade at least 1 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. 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. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over 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. St001298The number of repeated entries in the Lehmer code of a permutation. St001307The number of induced stars on four vertices in a graph. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. St001366The maximal multiplicity of a degree of a vertex of a graph. St001411The number of patterns 321 or 3412 in a permutation. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001469The holeyness of a permutation. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001552The number of inversions between excedances and fixed points of a permutation. St001565The number of arithmetic progressions of length 2 in a permutation. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001727The number of invisible inversions of a permutation. St001728The number of invisible descents of a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001839The number of excedances of a set partition. St001840The number of descents of a set partition. St001883The mutual visibility number of a graph. St000756The sum of the positions of the left to right maxima of a permutation. St001093The detour number of a graph. 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. St001782The order of rowmotion on the set of order ideals of a poset. 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 $eA$. St001404The number of distinct entries in a Gelfand Tsetlin pattern. St001644The dimension of a graph. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000873The aix statistic of a permutation. St001569The maximal modular displacement of a permutation. St000462The major index minus the number of excedences of a permutation. St001731The factorization defect of a permutation. St001805The maximal overlap of a cylindrical tableau associated with a semistandard tableau. St000550The number of modular elements of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001877Number of indecomposable injective modules with projective dimension 2. St000910The number of maximal chains of minimal length in a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St000307The number of rowmotion orbits of a poset. St001812The biclique partition number of a graph.