St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: St001343The dimension of the reduced incidence algebra of a poset. St000007The number of saliances of the permutation. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000025The number of initial rises of a Dyck path. St000031The number of cycles in the cycle decomposition of a permutation. St000053The number of valleys of the Dyck path. 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. St000141The maximum drop size of a permutation. St000147The largest part of an integer partition. St000153The number of adjacent cycles of a permutation. St000211The rank of the set partition. St000245The number of ascents of a permutation. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000507The number of ascents of a standard tableau. St000521The number of distinct subtrees of an ordered tree. St000632The jump number of the poset. St000672The number of minimal elements in Bruhat order not less than the permutation. St000703The number of deficiencies of a permutation. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000071The number of maximal chains in a poset. St000105The number of blocks in the set partition. St000167The number of leaves of an ordered tree. St000172The Grundy number of a graph. St000203The number of external nodes of a binary tree. St000300The number of independent sets of vertices of a graph. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000636The hull number of a graph. 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. St000733The row containing the largest entry of a standard tableau. St000784The maximum of the length and the largest part of the integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000839The largest opener of a set partition. St000975The length of the boundary minus the length of the trunk of an ordered tree. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001029The size of the core of a graph. St001050The number of terminal closers of a set partition. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001116The game chromatic number of a graph. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001286The annihilation number of a graph. 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. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001389The number of partitions of the same length below the given integer partition. St001462The number of factors of a standard tableaux under concatenation. St001494The Alon-Tarsi number of a graph. St001497The position of the largest weak excedence of a permutation. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001616The number of neutral elements in a lattice. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001670The connected partition number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001720The minimal length of a chain of small intervals in a lattice. St001809The index of the step at the first peak of maximal height in a Dyck path. St001820The size of the image of the pop stack sorting operator. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000028The number of stack-sorts needed to sort a permutation. St000052The number of valleys of a Dyck path not on the x-axis. St000069The number of maximal elements of a poset. St000157The number of descents of a standard tableau. St000214The number of adjacencies of a permutation. St000272The treewidth of a graph. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000340The number of non-final maximal constant sub-paths of length greater than one. St000362The size of a minimal vertex cover of a graph. St000378The diagonal inversion number of an integer partition. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000439The position of the first down step of a Dyck path. St000442The maximal area to the right of an up step of a Dyck path. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000536The pathwidth of a graph. St000662The staircase size of the code of a permutation. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000783The side length of the largest staircase partition fitting into a partition. 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 $c_{n-1}$. St000996The number of exclusive left-to-right maxima of a permutation. 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. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001090The number of pop-stack-sorts needed to sort a permutation. 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. St001176The size of a partition minus its first part. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001298The number of repeated entries in the Lehmer code of a permutation. 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. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001619The number of non-isomorphic sublattices of a lattice. St001622The number of join-irreducible elements of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001955The number of natural descents for set-valued two row standard Young tableaux. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000443The number of long tunnels of a Dyck path. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the 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. St000094The depth of an ordered tree. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St000015The number of peaks of a Dyck path. St000062The length of the longest increasing subsequence of the permutation. St000166The depth minus 1 of an ordered tree. St000325The width of the tree associated to a permutation. St000470The number of runs in a permutation. St000720The size of the largest partition in the oscillating tableau corresponding to the perfect matching. St000982The length of the longest constant subword. St000991The number of right-to-left minima of a permutation. St000120The number of left tunnels of a Dyck path. St000168The number of internal nodes of an ordered tree. St000238The number of indices that are not small weak excedances. St000306The bounce count of a Dyck path. St000316The number of non-left-to-right-maxima of a permutation. St000331The number of upper interactions of a Dyck path. St000332The positive inversions of an alternating sign matrix. St001046The maximal number of arcs nesting a given arc of a perfect matching. 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. 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. 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. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001180Number of indecomposable injective modules with projective dimension at most 1. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001717The largest size of an interval in a poset. St000056The decomposition (or block) number of a permutation. St000164The number of short pairs. St000213The number of weak exceedances (also weak excedences) of a permutation. St000239The number of small weak excedances. St000240The number of indices that are not small excedances. St000291The number of descents of a binary word. St000314The number of left-to-right-maxima of a permutation. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000381The largest part of an integer composition. St000390The number of runs of ones in a binary word. St000542The number of left-to-right-minima of a permutation. St000553The number of blocks of a graph. St000822The Hadwiger number of the graph. St000877The depth of the binary word interpreted as a path. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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. 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. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001461The number of topologically connected components of the chord diagram of a permutation. St001498The normalised height of a Nakayama algebra with magnitude 1. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001733The number of weak left to right maxima of a Dyck path. St001883The mutual visibility number of a graph. St001963The tree-depth of a graph. St000021The number of descents of a permutation. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000067The inversion number of the alternating sign matrix. St000080The rank of the poset. St000155The number of exceedances (also excedences) of a permutation. St000234The number of global ascents of a permutation. St000292The number of ascents of a binary word. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000864The number of circled entries of the shifted recording tableau of a permutation. St001047The maximal number of arcs crossing a given arc of a perfect matching. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001223Number of indecomposable projective non-injective modules P such that the modules X and Y in a an Auslander-Reiten sequence ending at P are torsionless. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001227The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001270The bandwidth of a graph. St001274The number of indecomposable injective modules with projective dimension equal to two. St001277The degeneracy of a graph. 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. St001358The largest degree of a regular subgraph of a graph. St001427The number of descents of a signed permutation. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. 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. St001726The number of visible inversions of a permutation. St001962The proper pathwidth of a graph. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000301The number of facets of the stable set polytope of a graph. St000326The position of the first one in a binary word after appending a 1 at the end. St000444The length of the maximal rise of a Dyck path. St000504The cardinality of the first block of a set partition. St000654The first descent of a permutation. St000668The least common multiple of the parts of the partition. St000678The number of up steps after the last double rise of a Dyck path. St000702The number of weak deficiencies of a permutation. St000708The product of the parts of an integer partition. St000738The first entry in the last row of a standard tableau. St000823The number of unsplittable factors of the set partition. St000925The number of topologically connected components of a set partition. St001062The maximal size of a block of a set partition. St001439The number of even weak deficiencies and of odd weak exceedences. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000035The number of left outer peaks of a permutation. St000054The first entry of the permutation. St000058The order of a permutation. St000063The number of linear extensions of a certain poset defined for an integer partition. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000068The number of minimal elements in a poset. St000084The number of subtrees. St000087The number of induced subgraphs. St000108The number of partitions contained in the given partition. St000149The number of cells of the partition whose leg is zero and arm is odd. St000150The floored half-sum of the multiplicities of a partition. St000201The number of leaf nodes in a binary tree. St000237The number of small exceedances. St000273The domination number of a graph. St000286The number of connected components of the complement of a graph. St000287The number of connected components of a graph. St000288The number of ones in a binary word. St000297The number of leading ones in a binary word. St000299The number of nonisomorphic vertex-induced subtrees. St000328The maximum number of child nodes in a tree. St000363The number of minimal vertex covers of a graph. St000382The first part of an integer composition. St000389The number of runs of ones of odd length in a binary word. St000392The length of the longest run of ones in a binary word. St000469The distinguishing number of a graph. St000482The (zero)-forcing number of a graph. St000532The total number of rook placements on a Ferrers board. St000544The cop number of a graph. St000651The maximal size of a rise in a permutation. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000722The number of different neighbourhoods in a graph. St000730The maximal arc length of a set partition. St000734The last entry in the first row of a standard tableau. St000740The last entry of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000744The length of the path to the largest entry in a standard Young tableau. St000746The number of pairs with odd minimum in a perfect matching. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000808The number of up steps of the associated bargraph. St000838The number of terminal right-hand endpoints when the vertices are written in order. St000843The decomposition number of a perfect matching. St000874The position of the last double rise in a Dyck path. St000876The number of factors in the Catalan decomposition of a binary word. St000885The number of critical steps in the Catalan decomposition of a binary word. St000916The packing number of a graph. St000926The clique-coclique number of a graph. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000971The smallest closer of a set partition. St001058The breadth of the ordered tree. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001316The domatic number of a graph. St001322The size of a minimal independent dominating set in a graph. St001330The hat guessing number of a graph. St001339The irredundance number of a graph. St001342The number of vertices in the center of a graph. St001363The Euler characteristic of a graph according to Knill. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001372The length of a longest cyclic run of ones of a binary word. St001400The total number of Littlewood-Richardson tableaux of given shape. 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. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001530The depth of a Dyck path. St001587Half of the largest even part of an integer partition. St001645The pebbling number of a connected graph. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001725The harmonious chromatic number of a graph. St001746The coalition number of a graph. St001828The Euler characteristic of a graph. St001829The common independence number of a graph. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St000004The major index of a permutation. St000012The area of a Dyck path. St000065The number of entries equal to -1 in an alternating sign matrix. St000081The number of edges of a graph. St000148The number of odd parts of a partition. St000156The Denert index of a permutation. St000160The multiplicity of the smallest part of a partition. St000161The sum of the sizes of the right subtrees of a binary tree. St000171The degree of the graph. St000209Maximum difference of elements in cycles. St000224The sorting index of a permutation. St000228The size of a partition. St000246The number of non-inversions of a permutation. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000305The inverse major index of a permutation. St000310The minimal degree of a vertex of a graph. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000336The leg major index of a standard tableau. St000377The dinv defect of an integer partition. St000384The maximal part of the shifted composition of an integer partition. St000386The number of factors DDU in a Dyck path. St000441The number of successions of a permutation. St000446The disorder of a permutation. St000454The largest eigenvalue of a graph if it is integral. St000459The hook length of the base cell of a partition. St000475The number of parts equal to 1 in a partition. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000519The largest length of a factor maximising the subword complexity. St000546The number of global descents of a permutation. St000548The number of different non-empty partial sums of an integer partition. St000585The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block. St000691The number of changes of a binary word. St000731The number of double exceedences of a permutation. St000741The Colin de Verdière graph invariant. St000778The metric dimension of a graph. St000834The number of right outer peaks of a permutation. St000840The number of closers smaller than the largest opener in a perfect matching. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000867The sum of the hook lengths in the first row of an integer partition. St000871The number of very big ascents of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001082The number of boxed occurrences of 123 in a permutation. St001083The number of boxed occurrences of 132 in a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001115The number of even descents of a permutation. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001127The sum of the squares of the parts of a partition. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. St001175The size of a partition minus the hook length of the base cell. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St001323The independence gap of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001391The disjunction number of a graph. St001397Number of pairs of incomparable elements in a finite poset. St001428The number of B-inversions of a signed permutation. St001479The number of bridges of a graph. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001644The dimension of a graph. St001651The Frankl number of a lattice. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001777The number of weak descents in an integer composition. St001869The maximum cut size of a graph. St001949The rigidity index of a graph. 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. St000083The number of left oriented leafs of a binary tree except the first one. St000354The number of recoils of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St001480The number of simple summands of the module J^2/J^3. St000144The pyramid weight of the Dyck path. St000489The number of cycles of a permutation of length at most 3. 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. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St000216The absolute length of a permutation. St000502The number of successions of a set partitions. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000728The dimension of a set partition. St000795The mad of a permutation. St000809The reduced reflection length of the permutation. St000831The number of indices that are either descents or recoils. St000837The number of ascents of distance 2 of a permutation. St000957The number of Bruhat lower covers of a permutation. 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). St000236The number of cyclical small weak excedances. St000259The diameter of a connected graph. St000488The number of cycles of a permutation of length at most 2. St000643The size of the largest orbit of antichains under Panyushev complementation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001512The minimum rank of a graph. St000061The number of nodes on the left branch of a binary tree. St000339The maf index of a permutation. St000485The length of the longest cycle of a permutation. St000552The number of cut vertices of a graph. St000619The number of cyclic descents of a permutation. St000675The number of centered multitunnels of a Dyck path. St000717The number of ordinal summands of a poset. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000906The length of the shortest maximal chain in a poset. St000990The first ascent of a permutation. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001093The detour number of a graph. St001346The number of parking functions that give the same permutation. St001692The number of vertices with higher degree than the average degree in a graph. St000159The number of distinct parts of the integer partition. St000359The number of occurrences of the pattern 23-1. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000495The number of inversions of distance at most 2 of a permutation. St000539The number of odd inversions of a permutation. St000653The last descent of a permutation. St000711The number of big exceedences of a permutation. St000794The mak of a permutation. St000984The number of boxes below precisely one peak. St000989The number of final rises of a permutation. St001077The prefix exchange distance of a permutation. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001812The biclique partition number of a graph. St001589The nesting number of a perfect matching. St001246The maximal difference between two consecutive entries of a permutation. St001590The crossing number of a perfect matching. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St000193The row of the unique '1' in the first column 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. St000652The maximal difference between successive positions of a permutation. St000956The maximal displacement of a permutation. St001863The number of weak excedances of a signed permutation. St000039The number of crossings of a permutation. St000317The cycle descent number of a permutation. St000358The number of occurrences of the pattern 31-2. St000710The number of big deficiencies of a permutation. St000732The number of double deficiencies of a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St000836The number of descents of distance 2 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. 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. St001429The number of negative entries in a signed permutation. St001552The number of inversions between excedances and fixed points of a permutation. St001668The number of points of the poset minus the width of the poset. St001948The number of augmented double ascents of a permutation. St000806The semiperimeter of the associated bargraph. St001626The number of maximal proper sublattices of a lattice. St001875The number of simple modules with projective dimension at most 1. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St001432The order dimension of the partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St000327The number of cover relations in a poset. St000460The hook length of the last cell along the main diagonal of an integer partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001360The number of covering relations in Young's lattice below a partition. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001933The largest multiplicity of a part in an integer partition. St000225Difference between largest and smallest parts in a partition. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St000863The length of the first row of the shifted shape of a permutation. St000898The number of maximal entries in the last diagonal of the monotone triangle. St001889The size of the connectivity set of a signed permutation. St001769The reflection length of a signed permutation. St001861The number of Bruhat lower covers of a permutation. St001894The depth of a signed permutation. St001896The number of right descents of a signed permutations. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001649The length of a longest trail in a graph. St000242The number of indices that are not cyclical small weak excedances. St000628The balance of a binary word. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000445The number of rises of length 1 of a Dyck path. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001864The number of excedances of a signed permutation. St000983The length of the longest alternating subword. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001712The number of natural descents of a standard Young tableau. St001905The number of preferred parking spots in a parking function less than the index of the car. St001935The number of ascents in a parking function. St001946The number of descents in a parking function. St001960The number of descents of a permutation minus one if its first entry is not one. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000896The number of zeros on the main diagonal of an alternating sign matrix. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St000942The number of critical left to right maxima of the parking functions. St001023Number of simple modules with projective dimension at most 3 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. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001523The degree of symmetry of a Dyck path. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St000647The number of big descents of a permutation. St000884The number of isolated descents of a permutation. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001126Number of simple module that are 1-regular 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. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001557The number of inversions of the second entry of a permutation. St001811The Castelnuovo-Mumford regularity of a permutation. St001870The number of positive entries followed by a negative entry in a signed permutation. St001893The flag descent of a signed permutation. St000681The Grundy value of Chomp on Ferrers diagrams. St000993The multiplicity of the largest part of an integer partition. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St000937The number of positive values of the symmetric group character corresponding to the partition. St000022The number of fixed points of a permutation. 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 $eA$. St000352The Elizalde-Pak rank of a permutation. 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 $eA$. St001060The distinguishing index of a graph. St000366The number of double descents of a permutation. St000904The maximal number of repetitions of an integer composition. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001866The nesting alignments of a signed permutation. St000254The nesting number of a set partition. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St000174The flush statistic of a semistandard tableau. St001728The number of invisible descents of a permutation. St001839The number of excedances of a set partition. St001840The number of descents of a set partition. St000824The sum of the number of descents and the number of recoils of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St000092The number of outer peaks of a permutation. St000099The number of valleys of a permutation, including the boundary. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000251The number of nonsingleton blocks of a set partition. St000253The crossing number of a set partition. St000674The number of hills of a Dyck path. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000785The number of distinct colouring schemes of a graph. St000910The number of maximal chains of minimal length in a poset. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001114The number of odd descents of a permutation. St001151The number of blocks with odd minimum. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. 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. St001665The number of pure excedances of a permutation. St001716The 1-improper chromatic number of a graph. St001729The number of visible descents of a permutation. St001737The number of descents of type 2 in a permutation. St001741The largest integer such that all patterns of this size are contained in the permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St001792The arboricity of a graph. St001806The upper middle entry of a permutation. St001807The lower middle entry of a permutation. St001928The number of non-overlapping descents in a permutation. St000023The number of inner peaks of a permutation. St000072The number of circled entries. St000091The descent variation of a composition. St000173The segment statistic of a semistandard tableau. St000196The number of occurrences of the contiguous pattern [[.,.],[.,. St000221The number of strong fixed points of a permutation. St000353The number of inner valleys of a permutation. St000365The number of double ascents of a permutation. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000486The number of cycles of length at least 3 of a permutation. St000646The number of big ascents of a permutation. St000663The number of right floats of a permutation. St000779The tier of 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. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001469The holeyness of a permutation. St001470The cyclic holeyness of a permutation. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in 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. St001624The breadth of a lattice. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000260The radius of a connected graph. St001638The book thickness of a graph. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St001571The Cartan determinant of the integer partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St000928The sum of the coefficients of the character polynomial of an integer partition. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. 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. St000455The second largest eigenvalue of a graph if it is integral. St000893The number of distinct diagonal sums of an alternating sign matrix. 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. St000478Another weight of a partition according to Alladi. St000075The orbit size of a standard tableau under promotion. St000089The absolute variation of a composition. St000090The variation of a composition. St000335The difference of lower and upper interactions. St000492The rob statistic of a set partition. St000498The lcs statistic of a set partition. St000522The number of 1-protected nodes of a rooted tree. St000577The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element. St001545The second Elser number of a connected graph. St000383The last part of an integer composition. St000589The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block. St000922The minimal number such that all substrings of this length are unique. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000973The length of the boundary of an ordered tree. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001416The length of a longest palindromic factor of a binary word. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001566The length of the longest arithmetic progression in a permutation. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001862The number of crossings of a signed permutation. St000100The number of linear extensions of a poset. St000230Sum of the minimal elements of the blocks of a set partition. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000456The monochromatic index of a connected graph. St000524The number of posets with the same order polynomial. St000525The number of posets with the same zeta polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000633The size of the automorphism group of a poset. St000635The number of strictly order preserving maps of a poset into itself. St000640The rank of the largest boolean interval in a poset. St000914The sum of the values of the Möbius function of a poset. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001890The maximum magnitude of the Möbius function of a poset. St000850The number of 1/2-balanced pairs in a poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St000736The last entry in the first row of a semistandard tableau. St001569The maximal modular displacement of a permutation. St000112The sum of the entries reduced by the index of their row in a semistandard tableau. St000177The number of free tiles in the pattern. St000178Number of free entries. St001520The number of strict 3-descents. St000739The first entry in the last row of a semistandard tableau. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001926Sparre Andersen's position of the maximum of a signed permutation. St000298The order dimension or Dushnik-Miller dimension of a poset. St000307The number of rowmotion orbits of a poset. St000909The number of maximal chains of maximal size in a poset. St000958The number of Bruhat factorizations of a permutation. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. 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 $K[x]/(x^n)$. St001487The number of inner corners of a skew partition. St001684The reduced word complexity of a permutation. St001722The number of minimal chains with small intervals between a binary word and the top element. St001823The Stasinski-Voll length of a signed permutation. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001904The length of the initial strictly increasing segment of a parking function. St001937The size of the center of a parking function. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. 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 $K[x]/(x^n)$. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001556The number of inversions of the third entry of a permutation. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001633The number of simple modules with projective dimension two in the incidence algebra of the poset. St001856The number of edges in the reduced word graph of a permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type.