St000120The number of left tunnels of a Dyck path. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000340The number of non-final maximal constant sub-paths of length greater than one. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St000031The number of cycles in the cycle decomposition of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000105The number of blocks in the set partition. St000157The number of descents of a standard tableau. St000164The number of short pairs. St000167The number of leaves of an ordered tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000239The number of small weak 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. St000325The width of the tree associated to a permutation. St000390The number of runs of ones in a binary word. St000470The number of runs in a permutation. St000542The number of left-to-right-minima of a permutation. St000912The number of maximal antichains in a poset. St000991The number of right-to-left minima of a permutation. 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. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St000021The number of descents of a permutation. St000052The number of valleys of a Dyck path not on the x-axis. St000155The number of exceedances (also excedences) of a permutation. St000168The number of internal nodes of an ordered tree. St000211The rank of the set partition. St000238The number of indices that are not small weak excedances. St000245The number of ascents of a permutation. St000292The number of ascents of a binary word. St000316The number of non-left-to-right-maxima of a permutation. St000332The positive inversions of an alternating sign matrix. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. 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. St000672The number of minimal elements in Bruhat order not less than the permutation. St000703The number of deficiencies of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000996The number of exclusive left-to-right maxima of a permutation. St001298The number of repeated entries in the Lehmer code of a permutation. St001489The maximum of the number of descents and the number of inverse descents. St000249The number of singletons (St000247) plus the number of antisingletons (St000248) of a set partition. St000507The number of ascents of a standard tableau. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001226The number of integers i such that the radical of the i-th indecomposable projective module has vanishing first extension group with the Jacobson radical J in the corresponding Nakayama algebra. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St000007The number of saliances of the permutation. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000035The number of left outer peaks of a permutation. St000056The decomposition (or block) number of a permutation. St000068The number of minimal elements in a poset. St000071The number of maximal chains in a poset. 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. St000147The largest part of an integer partition. St000153The number of adjacent cycles of a permutation. St000172The Grundy number of a graph. St000237The number of small exceedances. St000288The number of ones in a binary word. St000308The height of the tree associated to a permutation. St000389The number of runs of ones of odd length in a binary word. St000482The (zero)-forcing number of a graph. St000527The width of the poset. St000528The height of a poset. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000822The Hadwiger number of the graph. St000925The number of topologically connected components of a set partition. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001029The size of the core of a graph. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. 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. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. 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. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001616The number of neutral elements in a lattice. St001670The connected partition number of a graph. St001693The excess length of a longest path consisting of elements and blocks of a set partition. St001720The minimal length of a chain of small intervals in a lattice. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St001963The tree-depth of a graph. St000018The number of inversions of a permutation. St000019The cardinality of the support of a permutation. St000029The depth of a permutation. St000030The sum of the descent differences of a permutations. St000065The number of entries equal to -1 in an alternating sign matrix. St000080The rank of the poset. St000141The maximum drop size of a permutation. St000214The number of adjacencies of a permutation. St000234The number of global ascents of a permutation. St000272The treewidth of a graph. St000306The bounce count of a Dyck path. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000362The size of a minimal vertex cover of a graph. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000536The pathwidth of a graph. St000632The jump number of the poset. St000662The staircase size of the code of a permutation. St000834The number of right outer peaks of a permutation. St000871The number of very big ascents of a permutation. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001083The number of boxed occurrences of 132 in a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001153The number of blocks with even minimum in a set 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. 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. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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 $eA$. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. 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. St001358The largest degree of a regular subgraph of a graph. St001427The number of descents of a signed permutation. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001512The minimum rank of a graph. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001622The number of join-irreducible elements of a lattice. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000094The depth of an ordered tree. St000203The number of external nodes of a binary tree. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St000439The position of the first down step of a Dyck path. St000521The number of distinct subtrees of an ordered tree. St000636The hull number of a graph. 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. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001504The sum of all indegrees of vertices with indegree at least two in the resolution quiver of a Nakayama algebra corresponding to the Dyck path. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001654The monophonic hull number of a graph. St000013The height of a Dyck path. St000025The number of initial rises of a Dyck path. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000054The first entry of the permutation. St000063The number of linear extensions of a certain poset defined for an integer partition. St000069The number of maximal elements of a poset. St000084The number of subtrees. St000087The number of induced subgraphs. St000108The number of partitions contained in the given partition. St000144The pyramid weight of the Dyck path. St000146The Andrews-Garvan crank of a partition. St000166The depth minus 1 of an ordered tree. St000201The number of leaf nodes in a binary tree. St000228The size of a partition. St000240The number of indices that are not small excedances. 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. St000328The maximum number of child nodes in a tree. St000363The number of minimal vertex covers of a graph. St000378The diagonal inversion number of an integer partition. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000395The sum of the heights of the peaks of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000469The distinguishing number of a graph. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000532The total number of rook placements on a Ferrers board. St000544The cop number of a graph. St000553The number of blocks of a graph. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000722The number of different neighbourhoods in a graph. St000733The row containing the largest entry of a standard tableau. St000734The last entry in the first row of a standard tableau. St000738The first entry in the last row of a standard tableau. St000740The last entry of a permutation. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000808The number of up steps of the associated bargraph. St000843The decomposition number of a perfect matching. 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. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001058The breadth of the ordered tree. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001116The game chromatic number of a graph. St001128The exponens consonantiae of a partition. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama 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. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001280The number of parts of an integer partition that are at least two. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. 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. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001400The total number of Littlewood-Richardson tableaux of given shape. St001462The number of factors of a standard tableaux under concatenation. St001645The pebbling number of a connected graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. 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. St001733The number of weak left to right maxima of a Dyck path. St001746The coalition number of a graph. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001809The index of the step at the first peak of maximal height in a Dyck path. 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. St001883The mutual visibility number of a graph. St000004The major index of a permutation. St000012The area of a Dyck path. St000067The inversion number of the alternating sign matrix. St000081The number of edges of a graph. St000148The number of odd parts of a partition. 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. St000204The number of internal nodes of a binary tree. St000224The sorting index of a permutation. St000225Difference between largest and smallest parts in a partition. St000246The number of non-inversions of a permutation. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000331The number of upper interactions of a Dyck path. 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. 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. 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. St000691The number of changes of a binary word. St000741The Colin de Verdière graph invariant. St000778The metric dimension of a graph. St000784The maximum of the length and the largest part of the integer partition. St000864The number of circled entries of the shifted recording tableau of a permutation. St000867The sum of the hook lengths in the first row of an integer partition. St000868The aid statistic in the sense of Shareshian-Wachs. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St000992The alternating sum of the parts of an integer partition. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. 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. 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. 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. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. 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. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001644The dimension of a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001726The number of visible inversions of a permutation. St001777The number of weak descents in an integer composition. St001869The maximum cut size of a graph. St001949The rigidity index of a graph. St001962The proper pathwidth of a graph. St000702The number of weak deficiencies of a permutation. St000083The number of left oriented leafs of a binary tree except the first one. St000216The absolute length of a permutation. St000354The number of recoils of a permutation. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000809The reduced reflection length of the permutation. St000829The Ulam distance of a permutation to the identity permutation. St000061The number of nodes on the left branch of a binary tree. St000795The mad of a permutation. St000831The number of indices that are either descents or recoils. 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). St001480The number of simple summands of the module J^2/J^3. St000643The size of the largest orbit of antichains under Panyushev complementation. St001315The dissociation number of a graph. St000444The length of the maximal rise of a Dyck path. St000485The length of the longest cycle of a permutation. St000504The cardinality of the first block of a set partition. St000654The first descent of a permutation. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise 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. St001062The maximal size of a block of a set partition. St001346The number of parking functions that give the same permutation. St000442The maximal area to the right of an up step of a Dyck path. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000495The number of inversions of distance at most 2 of a permutation. St000502The number of successions of a set partitions. St000539The number of odd inversions of a permutation. St000653The last descent of a permutation. St000728The dimension of a set partition. St000730The maximal arc length of a set partition. St000874The position of the last double rise in a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St000984The number of boxes below precisely one peak. St000989The number of final rises of a permutation. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001812The biclique partition number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001323The independence gap of a graph. St001875The number of simple modules with projective dimension at most 1. St000356The number of occurrences of the pattern 13-2. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St000159The number of distinct parts of the integer partition. St001321The number of vertices of the largest induced subforest of a graph. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St000142The number of even parts of a partition. St000646The number of big ascents of a permutation. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St000619The number of cyclic descents of a permutation. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001432The order dimension of the partition. St000372The number of mid points of increasing subsequences of length 3 in a permutation. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000746The number of pairs with odd minimum in a perfect matching. St000474Dyson's crank of a partition. St000259The diameter of a connected graph. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St000143The largest repeated part of a partition. St000710The number of big deficiencies of a permutation. St000731The number of double exceedences of a permutation. St000260The radius of a connected graph. 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. St000711The number of big exceedences of a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000647The number of big descents of a permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St000312The number of leaves in a graph. St000028The number of stack-sorts needed to sort a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000223The number of nestings in the permutation. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000898The number of maximal entries in the last diagonal of the monotone triangle. St001430The number of positive entries in a signed permutation. St000358The number of occurrences of the pattern 31-2. St001152The number of pairs with even minimum in a perfect matching. St000236The number of cyclical small weak excedances. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St000242The number of indices that are not cyclical small weak excedances. St000299The number of nonisomorphic vertex-induced subtrees. 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. St000552The number of cut vertices of a graph. St001692The number of vertices with higher degree than the average degree in a graph. St000039The number of crossings of a permutation. St000317The cycle descent number of a permutation. St000732The number of double deficiencies of a permutation. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. 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. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001429The number of negative entries in a signed permutation. St001727The number of invisible inversions 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. St001782The order of rowmotion on the set of order ideals of a poset. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000264The girth of a graph, which is not a tree. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St001863The number of weak excedances of a signed permutation. 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. St001820The size of the image of the pop stack sorting operator. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000455The second largest eigenvalue of a graph if it is integral. St000837The number of ascents of distance 2 of a permutation. St000836The number of descents of distance 2 of a permutation. St001864The number of excedances of a signed permutation. St001866The nesting alignments of a signed permutation. St001090The number of pop-stack-sorts needed to sort a permutation. St000884The number of isolated descents of a permutation. St001060The distinguishing index of a graph. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St000445The number of rises of length 1 of a Dyck path. St000648The number of 2-excedences of a permutation. St001115The number of even descents of a permutation. St001712The number of natural descents of a standard Young tableau. St000942The number of critical left to right maxima of the parking functions. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001773The number of minimal elements in Bruhat order not less than the signed permutation. 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. 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. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001267The length of the Lyndon factorization of the binary word. St001649The length of a longest trail in a graph. St001343The dimension of the reduced incidence algebra of a poset. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001589The nesting number of a perfect matching. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000872The number of very big descents of a permutation. St001372The length of a longest cyclic run of ones 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. St001811The Castelnuovo-Mumford regularity of a permutation. St001874Lusztig's a-function for the symmetric group. St001964The interval resolution global dimension of a poset. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. St000392The length of the longest run of ones in a binary word. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001626The number of maximal proper sublattices of a lattice. St001624The breadth of a lattice. St000891The number of distinct diagonal sums of a permutation matrix. St001435The number of missing boxes in the first row. St001877Number of indecomposable injective modules with projective dimension 2. St000022The number of fixed points of a permutation.