St000153The number of adjacent cycles of a permutation. St000160The multiplicity of the smallest part of a partition. St000548The number of different non-empty partial sums of an integer partition. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000300The number of independent sets of vertices of a graph. St001330The hat guessing number of a graph. St000011The number of touch points (or returns) of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000093The cardinality of a maximal independent set of vertices of a graph. St000378The diagonal inversion number of an integer partition. St000439The position of the first down step of a Dyck path. St000507The number of ascents of a standard tableau. St000676The number of odd rises of a Dyck path. St000996The number of exclusive left-to-right maxima of a permutation. St000026The position of the first return of a Dyck path. St000054The first entry of the permutation. St000019The cardinality of the support of a permutation. St000141The maximum drop size of a permutation. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. 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. St000058The order of a permutation. St000068The number of minimal elements in a poset. St000110The number of permutations less than or equal to a permutation in left weak order. St000172The Grundy number of a graph. St000363The number of minimal vertex covers of a graph. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000505The biggest entry in the block containing the 1. St000527The width of the poset. St000655The length of the minimal rise of a Dyck path. St000657The smallest part of an integer composition. St000667The greatest common divisor of the parts of the 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. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000808The number of up steps of the associated bargraph. St000883The number of longest increasing subsequences of a permutation. St000899The maximal number of repetitions of an integer composition. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000904The maximal number of repetitions of an integer composition. St000909The number of maximal chains of maximal size in a poset. St001007Number of simple modules with projective dimension 1 in 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. 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. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001116The game chromatic number of a graph. St001389The number of partitions of the same length below the given integer partition. St001494The Alon-Tarsi number of a graph. St001571The Cartan determinant of the integer partition. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001670The connected partition number of a graph. St001675The number of parts equal to the part in the reversed composition. St001809The index of the step at the first peak of maximal height in a Dyck path. St001883The mutual visibility number of a graph. St001933The largest multiplicity of a part in an integer partition. St000171The degree of the graph. St000214The number of adjacencies of a permutation. St000234The number of global ascents of a permutation. St000245The number of ascents of a permutation. St000272The treewidth of a graph. 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. St000441The number of successions of a permutation. St000454The largest eigenvalue of a graph if it is integral. St000536The pathwidth of a graph. St000546The number of global descents of a permutation. St000632The jump number of the poset. St000662The staircase size of the code of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. 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. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001644The dimension of a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001759The Rajchgot index of a permutation. St001777The number of weak descents in an integer composition. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000294The number of distinct factors of a binary word. St000518The number of distinct subsequences in a binary word. St000521The number of distinct subtrees of an ordered tree. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000063The number of linear extensions of a certain poset defined for an integer partition. St000071The number of maximal chains in a poset. St000105The number of blocks in the set partition. St000108The number of partitions contained in the given partition. St000167The number of leaves of an ordered tree. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000273The domination number of a graph. St000288The number of ones in a binary word. St000290The major index of a binary word. St000296The length of the symmetric border of a binary word. St000297The number of leading ones in a binary word. St000392The length of the longest run of ones in a binary word. St000393The number of strictly increasing runs in a binary word. St000451The length of the longest pattern of the form k 1 2. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000468The Hosoya index of a graph. St000469The distinguishing number of a graph. St000482The (zero)-forcing number of a graph. St000528The height of a poset. St000532The total number of rook placements on a Ferrers board. St000544The cop number of a graph. St000627The exponent of a binary word. St000636The hull number of a graph. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000700The protection number of an ordered tree. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000775The multiplicity of the largest eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000839The largest opener of a set partition. 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. St000907The number of maximal antichains of minimal length in a poset. St000908The length of the shortest maximal antichain in a poset. St000911The number of maximal antichains of maximal size in a poset. St000912The number of maximal antichains in a poset. St000916The packing number of a graph. St000922The minimal number such that all substrings of this length are unique. St000926The clique-coclique number of a graph. St000971The smallest closer of a set partition. St000982The length of the longest constant subword. St001050The number of terminal closers of a set partition. St001051The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition. St001058The breadth of the ordered tree. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. 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: St001267The length of the Lyndon factorization of the binary word. St001312Number of parabolic noncrossing partitions indexed by the composition. St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001363The Euler characteristic of a graph according to Knill. St001372The length of a longest cyclic run of ones of a binary word. St001387Number of standard Young tableaux of the skew shape tracing the border of the given partition. St001400The total number of Littlewood-Richardson tableaux of given shape. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001437The flex of a binary word. St001462The number of factors of a standard tableaux under concatenation. St001485The modular major index of a binary word. St001527The cyclic permutation representation number of an integer partition. St001645The pebbling number of a connected graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001674The number of vertices of the largest induced star graph in the graph. 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. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001829The common independence number of a graph. St001884The number of borders of a binary word. St000008The major index of the composition. St000012The area of a Dyck path. St000018The number of inversions of a permutation. St000024The number of double up and double down steps of a Dyck path. St000053The number of valleys of the Dyck path. St000148The number of odd parts of a partition. St000157The number of descents of a standard tableau. St000211The rank of the set partition. St000228The size of a partition. St000237The number of small exceedances. St000246The number of non-inversions of a permutation. St000295The length of the border of a binary word. 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. St000384The maximal part of the shifted composition of an integer partition. 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. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000651The maximal size of a rise in a permutation. St000692Babson and Steingrímsson's statistic of a permutation. St000703The number of deficiencies of a permutation. St000778The metric dimension of a graph. St000784The maximum of the length and the largest part of the integer partition. St000867The sum of the hook lengths in the first row of an integer partition. St000877The depth of the binary word interpreted as a path. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001090The number of pop-stack-sorts needed to sort a permutation. St001091The number of parts in an integer partition whose next smaller part has the same size. St001127The sum of the squares of the parts of a partition. St001161The major index north count of a Dyck path. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001479The number of bridges of a graph. St001506Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra. St001541The Gini index of an integer partition. St001671Haglund's hag of a permutation. St001697The shifted natural comajor index of a standard Young tableau. St001721The degree of a binary word. St001826The maximal number of leaves on a vertex of a graph. St001949The rigidity index of a graph. St000326The position of the first one in a binary word after appending a 1 at the end. St001371The length of the longest Yamanouchi prefix of a binary word. St000308The height of the tree associated to a permutation. St000444The length of the maximal rise of a Dyck path. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000740The last entry of a permutation. St000770The major index of an integer partition when read from bottom to top. St000993The multiplicity of the largest part of an integer partition. St001268The size of the largest ordinal summand in the poset. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001399The distinguishing number of a poset. St001461The number of topologically connected components of the chord diagram of a permutation. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St001779The order of promotion on the set of linear extensions of a poset. St000391The sum of the positions of the ones in a binary word. St000442The maximal area to the right of an up step of a Dyck path. St000503The maximal difference between two elements in a common block. St000730The maximal arc length of a set partition. St000874The position of the last double rise in a Dyck path. St001298The number of repeated entries in the Lehmer code of a permutation. St001332The number of steps on the non-negative side of the walk associated with the permutation. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St000420The number of Dyck paths that are weakly above a Dyck path. St000504The cardinality of the first block of a set partition. St000675The number of centered multitunnels of a Dyck path. St000678The number of up steps after the last double rise of a Dyck path. St000729The minimal arc length of a set partition. St000815The number of semistandard Young tableaux of partition weight of given shape. St000823The number of unsplittable factors of the set partition. St000914The sum of the values of the Möbius function of a poset. St000925The number of topologically connected components of a set partition. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001062The maximal size of a block of a set partition. St001075The minimal size of a block of a set partition. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001463The number of distinct columns in the nullspace of a graph. St001497The position of the largest weak excedence of a permutation. St001808The box weight or horizontal decoration of a Dyck path. St000376The bounce deficit of a Dyck path. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000498The lcs statistic of a set partition. St000502The number of successions of a set partitions. St000567The sum of the products of all pairs of parts. St000653The last descent of a permutation. St000693The modular (standard) major index of a standard tableau. St000728The dimension of a set partition. St000794The mak of a permutation. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000932The number of occurrences of the pattern UDU in a Dyck path. St000947The major index east count of 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. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St000654The first descent of a permutation. St000702The number of weak deficiencies of a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000910The number of maximal chains of minimal length in a poset. St001498The normalised height of a Nakayama algebra with magnitude 1. St000461The rix statistic of a permutation. St000673The number of non-fixed points of a permutation. St000873The aix statistic 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. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000806The semiperimeter of the associated bargraph. 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. St001118The acyclic chromatic index of a graph. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. 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. St000681The Grundy value of Chomp on Ferrers diagrams. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000501The size of the first part in the decomposition of a permutation. St000470The number of runs in a permutation. St000542The number of left-to-right-minima of a permutation. St000209Maximum difference of elements in cycles. St000864The number of circled entries of the shifted recording tableau of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St001489The maximum of the number of descents and the number of inverse descents. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001316The domatic number of a graph. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001963The tree-depth of a graph. St000210Minimum over maximum difference of elements in cycles. St000446The disorder of a permutation. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001358The largest degree of a regular subgraph of a graph. St001375The pancake length of a permutation. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001579The number of cyclically simple transpositions decreasing the number of cyclic descents needed to sort a permutation. St001726The number of visible inversions of a permutation. St001962The proper pathwidth of a graph. St000301The number of facets of the stable set polytope of a graph. St001782The order of rowmotion on the set of order ideals of a poset. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000087The number of induced subgraphs. St000286The number of connected components of the complement of a graph. St000553The number of blocks of a graph. St000617The number of global maxima of a Dyck path. St000822The Hadwiger number of the graph. St001342The number of vertices in the center of a graph. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001717The largest size of an interval in a poset. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000306The bounce count of a Dyck path. St000310The minimal degree of a vertex of a graph. St000741The Colin de Verdière graph invariant. St001391The disjunction number of a graph. St001760The number of prefix or suffix reversals needed to sort a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000325The width of the tree associated to a permutation. St000990The first ascent of a permutation. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St000030The sum of the descent differences of a permutations. St000238The number of indices that are not small weak excedances. St000316The number of non-left-to-right-maxima 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. St000795The mad of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St000956The maximal displacement 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. 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. St000056The decomposition (or block) number of a permutation. St000062The length of the longest increasing subsequence of the permutation. St000239The number of small weak excedances. St000240The number of indices that are not small excedances. St000314The number of left-to-right-maxima of a permutation. St000335The difference of lower and upper interactions. St000443The number of long tunnels of a Dyck path. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000991The number of right-to-left minima of a permutation. 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. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001170Number of indecomposable injective modules whose socle has projective dimension at most g-1 when g denotes the global dimension in the corresponding Nakayama algebra. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001191Number of simple modules $S$ with $Ext_A^i(S,A)=0$ for all $i=0,1,...,g-1$ in the corresponding Nakayama algebra $A$ with global dimension $g$. 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. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001481The minimal height of a peak of a Dyck path. St000021The number of descents of a permutation. St000029The depth of a permutation. St000051The size of the left subtree of a binary tree. St000067The inversion number of the alternating sign matrix. St000133The "bounce" of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000224The sorting index of a permutation. St000305The inverse major index of a permutation. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000339The maf index of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000539The number of odd inversions of a permutation. St000809The reduced reflection length of the permutation. St000833The comajor index of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001077The prefix exchange distance of a permutation. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. 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. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001427The number of descents of a signed permutation. St000094The depth of an ordered tree. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St000014The number of parking functions supported by a Dyck path. St000015The number of peaks of a Dyck path. St000084The number of subtrees. St000086The number of subgraphs. St000100The number of linear extensions of a poset. St000166The depth minus 1 of an ordered tree. St000213The number of weak exceedances (also weak excedences) of a permutation. St000287The number of connected components of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000328The maximum number of child nodes in a tree. St000628The balance of a binary word. St000638The number of up-down runs of a permutation. St000717The number of ordinal summands of a poset. St000720The size of the largest partition in the oscillating tableau corresponding to the perfect matching. St000838The number of terminal right-hand endpoints when the vertices are written in order. St000906The length of the shortest maximal chain in a poset. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. 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. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001530The depth of a Dyck path. St001828The Euler characteristic of a graph. St000004The major index of a permutation. St000005The bounce statistic of a Dyck path. St000080The rank of the poset. St000120The number of left tunnels of a Dyck path. St000154The sum of the descent bottoms of a permutation. St000156The Denert index of a permutation. St000168The number of internal nodes of an ordered tree. St000304The load of a permutation. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000331The number of upper interactions of a Dyck path. St000332The positive inversions of an alternating sign matrix. St000494The number of inversions of distance at most 3 of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St001046The maximal number of arcs nesting a given arc of a perfect matching. St001117The game chromatic index of a graph. 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. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001205The number of non-simple indecomposable projective-injective modules of the algebra $eAe$ in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. 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. St001274The number of indecomposable injective modules with projective dimension equal to two. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001397Number of pairs of incomparable elements in a finite poset. St001428The number of B-inversions of a signed permutation. 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. St001869The maximum cut size of a graph. St001480The number of simple summands of the module J^2/J^3. St000061The number of nodes on the left branch of a binary tree. St001959The product of the heights of the peaks of a Dyck path. St000216The absolute length of a permutation. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St001346The number of parking functions that give the same permutation. St000083The number of left oriented leafs of a binary tree except the first one. St000849The number of 1/3-balanced pairs in a poset. St001965The number of decreasable positions in the corner sum matrix of an alternating sign matrix. 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. St001570The minimal number of edges to add to make a graph Hamiltonian. St001060The distinguishing index of a graph. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000840The number of closers smaller than the largest opener in a perfect matching. St001082The number of boxed occurrences of 123 in a permutation. St001812The biclique partition number of a graph. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St001132The number of leaves in the subtree whose sister has label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St000181The number of connected components of the Hasse diagram for the poset. St000193The row of the unique '1' in the first column of the alternating sign matrix. St001684The reduced word complexity of a permutation. St000060The greater neighbor of the maximum. 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. St001045The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching. St001555The order of a signed permutation. St001589The nesting number of a perfect matching. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000800The number of occurrences of the vincular pattern |231 in a permutation. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001429The number of negative entries in a signed permutation. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001434The number of negative sum pairs of a signed 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. St001948The number of augmented double ascents 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. St000327The number of cover relations in a poset. St001668The number of points of the poset minus the width of the poset. St001771The number of occurrences of the signed pattern 1-2 in a signed permutation. St001863The number of weak excedances of a signed permutation. St001866The nesting alignments of a signed permutation. St001882The number of occurrences of a type-B 231 pattern in a signed permutation. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001093The detour number of a graph. St001512The minimum rank of a graph. St000455The second largest eigenvalue of a graph if it is integral.