St000105The number of blocks in the set partition. St000167The number of leaves of an ordered tree. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000065The number of entries equal to -1 in an alternating sign matrix. St000159The number of distinct parts of the integer partition. St000340The number of non-final maximal constant sub-paths of length greater than one. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000521The number of distinct subtrees of an ordered tree. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001083The number of boxed occurrences of 132 in a permutation. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000925The number of topologically connected components of a set partition. St000442The maximal area to the right of an up step of a Dyck path. St000562The number of internal points of a set partition. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St000470The number of runs in a permutation. St000356The number of occurrences of the pattern 13-2. St000374The number of exclusive right-to-left minima of a permutation. St000703The number of deficiencies of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001489The maximum of the number of descents and the number of inverse descents. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St000619The number of cyclic descents of a permutation. St000354The number of recoils of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000742The number of big ascents of a permutation after prepending zero. St000871The number of very big ascents of a permutation. St000809The reduced reflection length of the permutation. St000670The reversal length of a permutation. St000884The number of isolated descents of a permutation. St000662The staircase size of the code of a permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000306The bounce count of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000646The number of big ascents of a permutation. St000711The number of big exceedences of a permutation. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000035The number of left outer peaks of a permutation. St000141The maximum drop size of a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St000647The number of big descents of a permutation. St000358The number of occurrences of the pattern 31-2. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000223The number of nestings in the permutation. St000031The number of cycles in the cycle decomposition of a permutation. St000245The number of ascents of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001964The interval resolution global dimension of a poset. St001928The number of non-overlapping descents in a permutation. St000534The number of 2-rises of a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St000451The length of the longest pattern of the form k 1 2. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St000007The number of saliances of the permutation. St000094The depth of an ordered tree. St001128The exponens consonantiae of a partition. St000542The number of left-to-right-minima of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St001389The number of partitions of the same length below the given integer partition. St001432The order dimension of the partition. St001571The Cartan determinant of the integer partition. 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. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000731The number of double exceedences of a permutation. St000366The number of double descents of a permutation. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St000036The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation. St001052The length of the exterior of a permutation. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. 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. St000732The number of double deficiencies of a permutation. St000706The product of the factorials of the multiplicities of an integer partition. St000993The multiplicity of the largest part of an integer partition. St000667The greatest common divisor of the parts of the partition. St001933The largest multiplicity of a part in an integer partition. St000026The position of the first return of a Dyck path. St000120The number of left tunnels of a Dyck path. St000291The number of descents of a binary word. St000297The number of leading ones in a binary word. St000331The number of upper interactions of a Dyck path. St000335The difference of lower and upper interactions. St000346The number of coarsenings of a partition. St000390The number of runs of ones in a binary word. St000392The length of the longest run of ones in a binary word. St000655The length of the minimal rise of a Dyck path. St000675The number of centered multitunnels of a Dyck path. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000733The row containing the largest entry of a standard tableau. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000876The number of factors in the Catalan decomposition of a binary word. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001006Number of simple modules with projective dimension equal to the global dimension of 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. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. 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. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001202Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra. 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 $eA$. 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. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. 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. 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. St001372The length of a longest cyclic run of ones 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. St001481The minimal height of a peak of a Dyck path. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001498The normalised height of a Nakayama algebra with magnitude 1. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001732The number of peaks visible from the left. St001884The number of borders of a binary word. St001462The number of factors of a standard tableaux under concatenation. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St000781The number of proper colouring schemes of a Ferrers diagram. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001597The Frobenius rank of a skew partition. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St000668The least common multiple of the parts of the partition. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000708The product of the parts of an integer partition. St000933The number of multipartitions of sizes given by an integer partition. St000872The number of very big descents of a permutation. St001568The smallest positive integer that does not appear twice in the partition. St001549The number of restricted non-inversions between exceedances. St001513The number of nested exceedences of a permutation. St001722The number of minimal chains with small intervals between a binary word and the top element. St000678The number of up steps after the last double rise of a Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St000744The length of the path to the largest entry in a standard Young tableau. St001280The number of parts of an integer partition that are at least two. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St000157The number of descents of a standard tableau. St000164The number of short pairs. St000292The number of ascents of a binary word. St000308The height of the tree associated to a permutation. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St000764The number of strong records in an integer composition. St000910The number of maximal chains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St000100The number of linear extensions of a poset. 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. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001256Number of simple reflexive modules that are 2-stable reflexive. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St000284The Plancherel distribution on integer partitions. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000618The number of self-evacuating tableaux of given shape. St000681The Grundy value of Chomp on Ferrers diagrams. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000934The 2-degree of an integer partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001780The order of promotion on the set of standard tableaux of given shape. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001924The number of cells in an integer partition whose arm and leg length coincide. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. 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. St001637The number of (upper) dissectors of a poset. St001668The number of points of the poset minus the width of the poset. St001890The maximum magnitude of the Möbius function of a poset. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000702The number of weak deficiencies of a permutation. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000628The balance of a binary word. St000720The size of the largest partition in the oscillating tableau corresponding to the perfect matching. St000982The length of the longest constant subword. St000332The positive inversions of an alternating sign matrix. St001046The maximal number of arcs nesting a given arc of a perfect matching. St001091The number of parts in an integer partition whose next smaller part has the same size. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St000443The number of long tunnels of a Dyck path. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000015The number of peaks of a Dyck path. St000325The width of the tree associated to a permutation. St000991The number of right-to-left minima of a permutation. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St000021The number of descents of a permutation. St000039The number of crossings of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000168The number of internal nodes of an ordered tree. St000238The number of indices that are not small weak excedances. St000242The number of indices that are not cyclical small weak excedances. St000316The number of non-left-to-right-maxima of a permutation. St000317The cycle descent number of a permutation. 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. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001298The number of repeated entries in the Lehmer code of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000166The depth minus 1 of an ordered tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000239The number of small weak excedances. St000314The number of left-to-right-maxima of a permutation. St000456The monochromatic index of a connected graph. 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. St001461The number of topologically connected components of the chord diagram of a permutation. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St001180Number of indecomposable injective modules with projective dimension at most 1. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001427The number of descents of a signed permutation. St001572The minimal number of edges to remove to make a graph bipartite. St001573The minimal number of edges to remove to make a graph triangle-free. 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). St001874Lusztig's a-function for the symmetric group. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St000083The number of left oriented leafs of a binary tree except the first one. St000216The absolute length of a permutation. St001344The neighbouring number of a permutation. St000824The sum of the number of descents and the number of recoils 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. St000787The number of flips required to make a perfect matching noncrossing. St000460The hook length of the last cell along the main diagonal of an integer partition. St000846The maximal number of elements covering an element of a poset. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. 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. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St000408The number of occurrences of the pattern 4231 in a permutation. St000842The breadth of a permutation. St001162The minimum jump of a permutation. St001726The number of visible inversions of a permutation. St001941The evaluation at 1 of the modified Kazhdan--Lusztig R polynomial (as in [1, Section 5. St000649The number of 3-excedences of a permutation. St000570The Edelman-Greene number of a permutation. St000360The number of occurrences of the pattern 32-1. St001613The binary logarithm of the size of the center of a lattice. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001845The number of join irreducibles minus the rank of a lattice. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001394The genus 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 $K[x]/(x^n)$. St000516The number of stretching pairs of a permutation. St001715The number of non-records in a permutation. St001591The number of graphs with the given composition of multiplicities of Laplacian eigenvalues. St001330The hat guessing number of a graph. St000359The number of occurrences of the pattern 23-1. St000788The number of nesting-similar perfect matchings of a perfect matching. St001043The depth of the leaf closest to the root in the binary unordered tree associated with the perfect matching. St000627The exponent of a binary word. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St000406The number of occurrences of the pattern 3241 in a permutation. St000355The number of occurrences of the pattern 21-3. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000694The number of affine bounded permutations that project to a given permutation. St001590The crossing number of a perfect matching. St001830The chord expansion number of a perfect matching. St001832The number of non-crossing perfect matchings in the chord expansion of a perfect matching. St001859The number of factors of the Stanley symmetric function associated with a permutation. St000658The number of rises of length 2 of a Dyck path. St000069The number of maximal elements of a poset. St001490The number of connected components of a skew partition. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000989The number of final rises of a permutation. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. St000883The number of longest increasing subsequences of a permutation. St000255The number of reduced Kogan faces with the permutation as type. St000404The number of occurrences of the pattern 3241 or of the pattern 4231 in a permutation. St000908The length of the shortest maximal antichain in a poset. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001735The number of permutations with the same set of runs. St000648The number of 2-excedences of a permutation. St001720The minimal length of a chain of small intervals in a lattice. St000802The number of occurrences of the vincular pattern |321 in a permutation. St001552The number of inversions between excedances and fixed points of a permutation. St001095The number of non-isomorphic posets with precisely one further covering relation. St001550The number of inversions between exceedances where the greater exceedance is linked. St001846The number of elements which do not have a complement in the lattice. St000768The number of peaks in an integer composition. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001130The number of two successive successions in a permutation. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001875The number of simple modules with projective dimension at most 1. St001877Number of indecomposable injective modules with projective dimension 2. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001301The first Betti number of the order complex associated with the poset. St001396Number of triples of incomparable elements in a finite poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St000590The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 1 is maximal, (2,3) are consecutive in a block. St000068The number of minimal elements in a poset. St001487The number of inner corners of a skew partition. St000181The number of connected components of the Hasse diagram for the poset. St000002The number of occurrences of the pattern 123 in a permutation. St000405The number of occurrences of the pattern 1324 in a permutation. St001621The number of atoms of a lattice. St000058The order of a permutation. St000260The radius of a connected graph. St001810The number of fixed points of a permutation smaller than its largest moved point. St001847The number of occurrences of the pattern 1432 in 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. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St001589The nesting number of a perfect matching. St000710The number of big deficiencies of a permutation. St001089Number of indecomposable projective non-injective modules minus the number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001152The number of pairs with even minimum in a perfect matching. St000092The number of outer peaks of a permutation. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000669The number of permutations obtained by switching ascents or descents of size 2. St000746The number of pairs with odd minimum in a perfect matching. St000789The number of crossing-similar perfect matchings of a perfect matching. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St000965The sum of the dimension of Ext^i(D(A),A) for i=1,. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001530The depth of a Dyck path. St001555The order of a signed permutation. St001665The number of pure excedances of a permutation. St001729The number of visible descents of a permutation. St001737The number of descents of type 2 in a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St000022The number of fixed points of a permutation. St000091The descent variation of a composition. St000119The number of occurrences of the pattern 321 in a permutation. St000353The number of inner valleys of a permutation. St000441The number of successions of a permutation. St000462The major index minus the number of excedences of a permutation. St000630The length of the shortest palindromic decomposition of a binary word. St000638The number of up-down runs of a permutation. St000665The number of rafts of a permutation. St000779The tier of a permutation. St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001181Number of indecomposable injective modules with grade at least 3 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. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. 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. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001470The cyclic holeyness of a permutation. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001727The number of invisible inversions of a permutation. St001728The number of invisible descents of a permutation. St001769The reflection length of a signed permutation. St001862The number of crossings of a signed permutation. St001864The number of excedances of a signed permutation. St001896The number of right descents of a signed permutations. St001965The number of decreasable positions in the corner sum matrix of an alternating sign matrix. St001435The number of missing boxes in the first row. St001811The Castelnuovo-Mumford regularity of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St000527The width of the poset. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000219The number of occurrences of the pattern 231 in a permutation. St000440The number of occurrences of the pattern 4132 or of the pattern 4231 in a permutation. St000893The number of distinct diagonal sums of an alternating sign matrix. 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 $eA$. St001520The number of strict 3-descents. St001557The number of inversions of the second entry of a permutation. St001948The number of augmented double ascents of a permutation. St000256The number of parts from which one can substract 2 and still get an integer partition. St000660The number of rises of length at least 3 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 $eA$. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000298The order dimension or Dushnik-Miller dimension of a poset. St000307The number of rowmotion orbits of a poset. St001399The distinguishing number of a poset. St000632The jump number of the poset. St000629The defect of a binary word. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001271The competition number of a graph. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000862The number of parts of the shifted shape of a permutation. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St001533The largest coefficient of the Poincare polynomial of the poset cone. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St000891The number of distinct diagonal sums of a permutation matrix. St000407The number of occurrences of the pattern 2143 in a permutation. St000455The second largest eigenvalue of a graph if it is integral. St000666The number of right tethers of a permutation. St001866The nesting alignments of a signed permutation. St001868The number of alignments of type NE of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St000750The number of occurrences of the pattern 4213 in a permutation. St001663The number of occurrences of the Hertzsprung pattern 132 in a permutation. St000850The number of 1/2-balanced pairs in a poset. St000741The Colin de Verdière graph invariant. St000623The number of occurrences of the pattern 52341 in a permutation. St000650The number of 3-rises of a permutation. St000664The number of right ropes of a permutation. St000751The number of occurrences of either of the pattern 2143 or 2143 in a permutation. St000383The last part of an integer composition. St001867The number of alignments of type EN of a signed permutation. St001059Number of occurrences of the patterns 41352,42351,51342,52341 in a permutation. St000805The number of peaks of the associated bargraph. St000900The minimal number of repetitions of a part in an integer composition. 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 $c_{n−1}$. St001569The maximal modular displacement of a permutation. St001171The vector space dimension of $Ext_A^1(I_o,A)$ when $I_o$ is the tilting module corresponding to the permutation $o$ in the Auslander algebra $A$ of $K[x]/(x^n)$. 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. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000486The number of cycles of length at least 3 of a permutation. St000654The first descent of a permutation. St000902 The minimal number of repetitions of an integer composition. St000905The number of different multiplicities of parts of an integer composition. St000983The length of the longest alternating subword. St001313The number of Dyck paths above the lattice path given by a binary word. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001413Half the length of the longest even length palindromic prefix of a binary word. St001661Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation. St001768The number of reduced words of a signed permutation. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001889The size of the connectivity set of a signed permutation. St000034The maximum defect over any reduced expression for a permutation and any subexpression. St000338The number of pixed points of a permutation. St000348The non-inversion sum of a binary word. St000365The number of double ascents of a permutation. St000367The number of simsun double descents of a permutation. St000461The rix statistic of a permutation. St000488The number of cycles of a permutation of length at most 2. St000546The number of global descents of a permutation. St000661The number of rises of length 3 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. St000709The number of occurrences of 14-2-3 or 14-3-2. St000760The length of the longest strictly decreasing subsequence of parts of an integer composition. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000877The depth of the binary word interpreted as a path. St000951The dimension of $Ext^{1}(D(A),A)$ of the corresponding LNakayama algebra. St000990The first ascent of a permutation. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001488The number of corners of a skew partition. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001705The number of occurrences of the pattern 2413 in a permutation. St001712The number of natural descents of a standard Young tableau. St001772The number of occurrences of the signed pattern 12 in a signed permutation. St001821The sorting index of a signed permutation. St001823The Stasinski-Voll length of a signed permutation. St001856The number of edges in the reduced word graph of a permutation. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St000011The number of touch points (or returns) of a Dyck path. St000729The minimal arc length of a set partition. St000889The number of alternating sign matrices with the same antidiagonal sums. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001786The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order. St000296The length of the symmetric border of a binary word. St000326The position of the first one in a binary word after appending a 1 at the end. St000498The lcs statistic of a set partition. St000557The number of occurrences of the pattern {{1},{2},{3}} in a set partition. St000563The number of overlapping pairs of blocks of a set partition. St000575The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element and 2 a singleton. St000576The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal and 2 a minimal element. St000580The number of occurrences of the pattern {{1},{2},{3}} such that 2 is minimal, 3 is maximal. St000583The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 1, 2 are maximal. St000584The number of occurrences of the pattern {{1},{2},{3}} such that 1 is minimal, 3 is maximal. St000587The number of occurrences of the pattern {{1},{2},{3}} such that 1 is minimal. St000588The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are minimal, 2 is maximal. St000591The number of occurrences of the pattern {{1},{2},{3}} such that 2 is maximal. St000592The number of occurrences of the pattern {{1},{2},{3}} such that 1 is maximal. St000593The number of occurrences of the pattern {{1},{2},{3}} such that 1,2 are minimal. St000594The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) are consecutive in a block. St000596The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 1 is maximal. St000603The number of occurrences of the pattern {{1},{2},{3}} such that 2,3 are minimal. St000604The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 2 is maximal. St000608The number of occurrences of the pattern {{1},{2},{3}} such that 1,2 are minimal, 3 is maximal. St000615The number of occurrences of the pattern {{1},{2},{3}} such that 1,3 are maximal. St001438The number of missing boxes of a skew partition. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St000054The first entry of the permutation. St000635The number of strictly order preserving maps of a poset into itself. St000352The Elizalde-Pak rank of a permutation.