St000012The area of a Dyck path. St000013The height of a Dyck path. St000015The number of peaks of a Dyck path. St000025The number of initial rises of a Dyck path. 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. St000141The maximum drop size of a permutation. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000325The width of the tree associated to a permutation. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000383The last part of an integer composition. St000443The number of long tunnels of a Dyck path. St000470The number of runs in a permutation. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000505The biggest entry in the block containing the 1. St000507The number of ascents of a standard tableau. St000542The number of left-to-right-minima of a permutation. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000691The number of changes of a binary word. 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. 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. 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. St000971The smallest closer of a set partition. St000991The number of right-to-left minima of a permutation. St001007Number of simple modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. 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. St001187The number of simple modules with grade at least one 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. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001437The flex of a binary word. St001461The number of topologically connected components of the chord diagram of a permutation. St001462The number of factors of a standard tableaux under concatenation. St001530The depth of a Dyck path. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St001809The index of the step at the first peak of maximal height in a Dyck path. St000021The number of descents of a permutation. St000024The number of double up and double down steps of a Dyck path. St000028The number of stack-sorts needed to sort a permutation. St000053The number of valleys of the Dyck path. St000054The first entry of the permutation. St000120The number of left tunnels of a Dyck path. St000155The number of exceedances (also excedences) of a permutation. St000331The number of upper interactions of a Dyck path. St000439The position of the first down step of a Dyck path. St000446The disorder of a permutation. St000519The largest length of a factor maximising the subword complexity. St000546The number of global descents of a permutation. St000651The maximal size of a rise in a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001180Number of indecomposable injective modules with projective dimension at most 1. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001215Let X be the direct sum of all simple modules 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. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001372The length of a longest cyclic run of ones of a binary word. St001489The maximum of the number of descents and the number of inverse descents. 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. 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. 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. St001777The number of weak descents in an integer composition. St000806The semiperimeter of the associated bargraph. St000011The number of touch points (or returns) of a Dyck path. St000019The cardinality of the support of a permutation. St000041The number of nestings of a perfect matching. St000056The decomposition (or block) number of a permutation. St000058The order of a permutation. St000066The column of the unique '1' in the first row of the alternating sign matrix. St000068The number of minimal elements in a poset. St000069The number of maximal elements of 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. St000110The number of permutations less than or equal to a permutation in left weak order. St000153The number of adjacent cycles 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. St000164The number of short pairs. St000166The depth minus 1 of an ordered tree. St000167The number of leaves of an ordered tree. St000172The Grundy number of a graph. St000213The number of weak exceedances (also weak excedences) of a permutation. St000228The size of a partition. St000239The number of small weak 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. St000291The number of descents of a binary word. St000297The number of leading ones in a binary word. St000299The number of nonisomorphic vertex-induced subtrees. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000390The number of runs of 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. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000442The maximal area to the right of an up step of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000501The size of the first part in the decomposition of a permutation. St000503The maximal difference between two elements in a common block. St000527The width of the poset. St000528The height of a poset. St000544The cop number of a graph. St000548The number of different non-empty partial sums of an integer partition. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000667The greatest common divisor of the parts of the partition. St000678The number of up steps after the last double rise of a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000720The size of the largest partition in the oscillating tableau corresponding to the perfect matching. St000722The number of different neighbourhoods in a graph. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000730The maximal arc length of a set partition. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000822The Hadwiger number of the graph. St000839The largest opener of a set partition. St000874The position of the last double rise in a Dyck path. St000908The length of the shortest maximal antichain in a poset. St000912The number of maximal antichains in a poset. St000916The packing number of a graph. St000932The number of occurrences of the pattern UDU in a Dyck path. St000982The length of the longest constant subword. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001029The size of the core of a graph. 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. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001116The game 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. 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: St001235The global dimension of the corresponding Comp-Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. 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. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001343The dimension of the reduced incidence algebra of a poset. St001363The Euler characteristic of a graph according to Knill. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001389The number of partitions of the same length below the given integer partition. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001464The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise. St001494The Alon-Tarsi number of a graph. St001497The position of the largest weak excedence of a permutation. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001558The number of transpositions that are smaller or equal to a permutation in Bruhat order. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001670The connected partition number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001717The largest size of an interval in a poset. St001733The number of weak left to right maxima of a Dyck path. 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. St001933The largest multiplicity of a part in an integer partition. St001963The tree-depth of a graph. St000004The major index of a permutation. St000026The position of the first return of a Dyck path. St000052The number of valleys of a Dyck path not on the x-axis. St000080The rank of the poset. St000094The depth of an ordered tree. St000133The "bounce" of a permutation. St000168The number of internal nodes of an ordered tree. St000169The cocharge of a standard tableau. St000209Maximum difference of elements in cycles. St000211The rank of the set partition. St000234The number of global ascents of a permutation. St000238The number of indices that are not small weak excedances. St000245The number of ascents of a permutation. St000272The treewidth of a graph. St000292The number of ascents of a binary word. St000304The load of a permutation. St000305The inverse major index of a permutation. St000306The bounce count of a Dyck path. St000316The number of non-left-to-right-maxima of a permutation. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000332The positive inversions of an alternating sign matrix. St000337The lec statistic, the sum of the inversion numbers of the hook factors of a permutation. St000340The number of non-final maximal constant sub-paths of length greater than one. St000356The number of occurrences of the pattern 13-2. St000362The size of a minimal vertex cover of a graph. St000374The number of exclusive right-to-left minima of a permutation. St000444The length of the maximal rise of a Dyck path. St000445The number of rises of length 1 of a Dyck path. St000459The hook length of the base cell of a partition. St000460The hook length of the last cell along the main diagonal of an integer partition. St000521The number of distinct subtrees of an ordered tree. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000536The pathwidth of a graph. St000632The jump number of the poset. St000653The last descent of a permutation. St000662The staircase size of the code of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000703The number of deficiencies of a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000783The side length of the largest staircase partition fitting into a partition. St000820The number of compositions obtained by rotating the composition. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000864The number of circled entries of the shifted recording tableau of a permutation. St000868The aid statistic in the sense of Shareshian-Wachs. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000931The number of occurrences of the pattern UUU in a Dyck path. St000969We make a CNakayama algebra out of the LNakayama algebra (corresponding to the Dyck path) $[c_0,c_1,...,c_{n-1}]$ by adding $c_0$ to $c_{n-1}$. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001046The maximal number of arcs nesting a given arc of a perfect matching. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. 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. 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. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. 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 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 $eA$. 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. 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. 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. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001298The number of repeated entries in the Lehmer code of a permutation. St001358The largest degree of a regular subgraph of a graph. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001427The number of descents of a signed permutation. St001484The number of singletons of an integer partition. St001584The area statistic between a Dyck path and its bounce path. St001697The shifted natural comajor index of a standard Young tableau. St001726The number of visible inversions of a permutation. St001814The number of partitions interlacing the given partition. St001907The number of Bastidas - Hohlweg - Saliola excedances of a signed permutation. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001486The number of corners of the ribbon associated with an integer composition. St000326The position of the first one in a binary word after appending a 1 at the end. St000504The cardinality of the first block of a set partition. St000702The number of weak deficiencies of a permutation. St000823The number of unsplittable factors of the set partition. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000925The number of topologically connected components of a set partition. St001062The maximal size of a block of a set partition. 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. St000831The number of indices that are either descents or recoils. St000989The number of final rises of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St000018The number of inversions of a permutation. St000061The number of nodes on the left branch of a binary tree. St000485The length of the longest cycle of a permutation. St000652The maximal difference between successive positions of a permutation. St000654The first descent of a permutation. St000668The least common multiple of the parts of the partition. St000675The number of centered multitunnels of a Dyck path. St000708The product of the parts of an integer partition. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000746The number of pairs with odd minimum in a perfect matching. St000770The major index of an integer partition when read from bottom to top. St000844The size of the largest block in the direct sum decomposition of a permutation. St000906The length of the shortest maximal chain in a poset. St000914The sum of the values of the Möbius function of a poset. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St000990The first ascent of a permutation. St000993The multiplicity of the largest part of an integer partition. St001346The number of parking functions that give the same permutation. St001397Number of pairs of incomparable elements in a finite poset. St000502The number of successions of a set partitions. St000673The number of non-fixed points of a permutation. St000787The number of flips required to make a perfect matching noncrossing. St000794The mak of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000833The comajor index of a permutation. St000837The number of ascents of distance 2 of a permutation. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001268The size of the largest ordinal summand in the poset. St001480The number of simple summands of the module J^2/J^3. St001727The number of invisible inversions of a permutation. St001812The biclique partition number of a graph. St000006The dinv of a Dyck path. St000060The greater neighbor of the maximum. St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2. St000005The bounce statistic of a Dyck path. St000051The size of the left subtree of a binary tree. St000057The Shynar inversion number of a standard tableau. St000067The inversion number of the alternating sign matrix. St000076The rank of the alternating sign matrix in the alternating sign matrix poset. St000204The number of internal nodes of a binary tree. St000246The number of non-inversions of a permutation. St001571The Cartan determinant of the integer partition. St000159The number of distinct parts of the integer partition. St000235The number of indices that are not cyclical small weak excedances. St000240The number of indices that are not small excedances. St000692Babson and Steingrímsson's statistic of a permutation. St000836The number of descents of distance 2 of a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000873The aix statistic of a permutation. St000895The number of ones on the main diagonal of an alternating sign matrix. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001636The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset. St000643The size of the largest orbit of antichains under Panyushev complementation. St001330The hat guessing number of a graph. St000840The number of closers smaller than the largest opener in a perfect matching. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. 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. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. 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. St000384The maximal part of the shifted composition of an integer partition. St000784The maximum of the length and the largest part of the integer partition. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. 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. St000710The number of big deficiencies of a permutation. St001152The number of pairs with even minimum in a perfect matching. St000050The depth or height of a binary tree. St000089The absolute variation of a composition. St000144The pyramid weight of the Dyck path. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000395The sum of the heights of the peaks of a Dyck path. St000626The minimal period of a binary word. St000657The smallest part of an integer composition. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001136The largest label with larger sister in the leaf labelled binary unordered tree associated with the perfect matching. St001161The major index north count of a Dyck path. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001415The length of the longest palindromic prefix of a binary word. St001523The degree of symmetry of a Dyck path. St001554The number of distinct nonempty subtrees of a binary tree. St001555The order of a signed permutation. St001589The nesting number of a perfect matching. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St000039The number of crossings of a permutation. St000317The cycle descent number of a permutation. St000338The number of pixed points of a permutation. St000358The number of occurrences of the pattern 31-2. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000711The number of big exceedences of a permutation. St000719The number of alignments in a perfect matching. St000800The number of occurrences of the vincular pattern |231 in 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. St001108The 2-dynamic chromatic number of a graph. 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. St001219Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001557The number of inversions of the second entry of a permutation. St001684The reduced word complexity of a permutation. St001692The number of vertices with higher degree than the average degree in a graph. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001965The number of decreasable positions in the corner sum matrix of an alternating sign matrix. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001746The coalition number of a graph. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000898The number of maximal entries in the last diagonal of the monotone triangle. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001962The proper pathwidth of a graph. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001668The number of points of the poset minus the width of the poset. St001948The number of augmented double ascents of a permutation. 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. St000454The largest eigenvalue of a graph if it is integral. St001769The reflection length of a signed permutation. St001864The number of excedances of a signed permutation. St001637The number of (upper) dissectors of a poset. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St000736The last entry in the first row of a semistandard tableau. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St001638The book thickness of a graph. St000181The number of connected components of the Hasse diagram for the poset. St000680The Grundy value for Hackendot on posets. St000981The length of the longest zigzag subpath. St001074The number of inversions of the cyclic embedding of a permutation. St001644The dimension of a graph. St001959The product of the heights of the peaks of a Dyck path. St000628The balance of a binary word. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St001414Half the length of the longest odd length palindromic prefix of a binary word. 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 $eA$. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001937The size of the center of a parking function. St000682The Grundy value of Welter's game on a binary word. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001712The number of natural descents of a standard Young tableau. St000014The number of parking functions supported by a Dyck path. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000294The number of distinct factors of a binary word. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000420The number of Dyck paths that are weakly above a Dyck path. St000518The number of distinct subsequences in a binary word. St000529The number of permutations whose descent word is the given binary word. St000532The total number of rook placements on a Ferrers board. St000543The size of the conjugacy class of a binary word. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St001060The distinguishing index of a graph. 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. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001400The total number of Littlewood-Richardson tableaux of given shape. 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. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001658The total number of rook placements on a Ferrers board. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St000766The number of inversions of an integer composition. St000942The number of critical left to right maxima of the parking functions. 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 $eA$. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001863The number of weak excedances of a signed permutation. St001904The length of the initial strictly increasing segment of a parking function. St001423The number of distinct cubes in a binary word. St001424The number of distinct squares in a binary word. St001488The number of corners of a skew partition. St001520The number of strict 3-descents. St001556The number of inversions of the third entry of a permutation. St001745The number of occurrences of the arrow pattern 13 with an arrow from 1 to 2 in a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St000735The last entry on the main diagonal of a standard tableau. 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. St001896The number of right descents of a signed permutations. St000741The Colin de Verdière graph invariant. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001645The pebbling number of a connected graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St001946The number of descents in a parking function. St000456The monochromatic index of a connected graph. St001096The size of the overlap set of a permutation. St000123The difference in Coxeter length of a permutation and its image under the Simion-Schmidt map. St000223The number of nestings in the permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001115The number of even descents of a permutation. St001394The genus of a permutation. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St000815The number of semistandard Young tableaux of partition weight of given shape. St000933The number of multipartitions of sizes given by an integer partition. St000522The number of 1-protected nodes of a rooted tree. St000973The length of the boundary of an ordered tree. St000975The length of the boundary minus the length of the trunk of an ordered tree. St000939The number of characters of the symmetric group whose value on the partition is positive. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000438The position of the last up step in a Dyck path. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000707The product of the factorials of the parts. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000762The sum of the positions of the weak records of an integer composition. St000937The number of positive values of the symmetric group character corresponding to the partition. St001118The acyclic chromatic index of a graph. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000091The descent variation of a composition. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St001114The number of odd descents of a permutation. St001128The exponens consonantiae of a partition. St001151The number of blocks with odd minimum. St001665The number of pure excedances of a permutation. St001737The number of descents of type 2 in a permutation. St001778The largest greatest common divisor of an element and its image in a permutation. St001859The number of factors of the Stanley symmetric function associated with a permutation. St000043The number of crossings plus two-nestings of a perfect matching. St000173The segment statistic of a semistandard tableau. St000360The number of occurrences of the pattern 32-1. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000491The number of inversions of a set partition. St000565The major index of a set partition. St000581The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 2 is maximal. St000585The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal, (1,3) are consecutive in a block. St000594The number of occurrences of the pattern {{1,3},{2}} such that 1,2 are minimal, (1,3) are consecutive in a block. St000610The number of occurrences of the pattern {{1,3},{2}} such that 2 is maximal. St000613The number of occurrences of the pattern {{1,3},{2}} such that 2 is minimal, 3 is maximal, (1,3) are consecutive in a block. St000650The number of 3-rises of a permutation. St001403The number of vertical separators in a permutation. St001513The number of nested exceedences of a permutation. St001549The number of restricted non-inversions between exceedances. St001781The interlacing number of a set partition. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001843The Z-index of a set partition. St000352The Elizalde-Pak rank of a permutation. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000567The sum of the products of all pairs of parts. St000681The Grundy value of Chomp on Ferrers diagrams. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000834The number of right outer peaks of a permutation. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St001568The smallest positive integer that does not appear twice in the partition. St000483The number of times a permutation switches from increasing to decreasing or decreasing to increasing. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001487The number of inner corners of a skew partition. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000455The second largest eigenvalue of a graph if it is integral. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St000023The number of inner peaks of a permutation. St000090The variation of a composition. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000264The girth of a graph, which is not a tree. St000492The rob statistic of a set partition. St000497The lcb statistic of a set partition. St000498The lcs statistic of a set partition. St000562The number of internal points of a set partition. St000577The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element. St000597The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, (2,3) are consecutive in a block. St000614The number of occurrences of the pattern {{1},{2,3}} such that 1 is minimal, 3 is maximal, (2,3) are consecutive in a block. St000624The normalized sum of the minimal distances to a greater element. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000706The product of the factorials of the multiplicities of an integer partition. St000779The tier of a permutation. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001469The holeyness of a permutation. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St001722The number of minimal chains with small intervals between a binary word and the top element. St001935The number of ascents in a parking function. St000075The orbit size of a standard tableau under promotion. St000099The number of valleys of a permutation, including the boundary. St000365The number of double ascents of a permutation. St000589The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block. St000606The number of occurrences of the pattern {{1},{2,3}} such that 1,3 are maximal, (2,3) are consecutive in a block. St000611The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal. St000709The number of occurrences of 14-2-3 or 14-3-2. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001867The number of alignments of type EN of a signed permutation. St001868The number of alignments of type NE of a signed permutation. St000230Sum of the minimal elements of the blocks of a set partition. St001375The pancake length of a permutation. St001516The number of cyclic bonds of a 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. St001099The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees. St001100The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled trees. 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 $K[x]/(x^n)$. St001569The maximal modular displacement of a permutation. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. 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. St000307The number of rowmotion orbits of a poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St001811The Castelnuovo-Mumford regularity of a permutation. St000717The number of ordinal summands of a poset. St000718The largest Laplacian eigenvalue of a graph if it is integral.