St000445The number of rises of length 1 of a Dyck path. St000658The number of rises of length 2 of a Dyck path. St000885The number of critical steps in the Catalan decomposition of a binary word. St000932The number of occurrences of the pattern UDU in a Dyck path. St000989The number of final rises of a permutation. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. St001114The number of odd descents of a permutation. St001172The number of 1-rises at odd height of a Dyck path. St001189The number of simple modules with dominant and codominant dimension equal to zero in the Nakayama algebra corresponding to the Dyck path. 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. 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. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001413Half the length of the longest even length palindromic prefix of a binary word. St001510The number of self-evacuating linear extensions of a finite poset. St001524The degree of symmetry of a binary word. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001777The number of weak descents in an integer composition. St001955The number of natural descents for set-valued two row standard Young tableaux. St000011The number of touch points (or returns) of a Dyck path. St000025The number of initial rises of a Dyck path. St000335The difference of lower and upper interactions. St000675The number of centered multitunnels of a Dyck path. St000676The number of odd rises of a Dyck path. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St000990The first ascent 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. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001050The number of terminal closers of a set partition. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension in the corresponding Nakayama algebra. St001184Number of indecomposable injective modules with grade at least 1 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. St001210Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path. St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001439The number of even weak deficiencies and of odd weak exceedences. St001481The minimal height of a peak of a Dyck path. St001733The number of weak left to right maxima of a Dyck path. St000439The position of the first down step of 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 $c_{n-1}$. St001180Number of indecomposable injective modules with projective dimension at most 1. 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. St000012The area of a Dyck path. St000022The number of fixed points 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. St000039The number of crossings of a permutation. St000053The number of valleys of the Dyck path. St000083The number of left oriented leafs of a binary tree except the first one. St000120The number of left tunnels of a Dyck path. St000124The cardinality of the preimage of the Simion-Schmidt map. St000148The number of odd parts of a partition. St000153The number of adjacent cycles of a permutation. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000220The number of occurrences of the pattern 132 in a permutation. St000221The number of strong fixed points of a permutation. St000222The number of alignments in the permutation. St000234The number of global ascents of a permutation. St000237The number of small exceedances. St000239The number of small weak excedances. St000241The number of cyclical small excedances. St000245The number of ascents of a permutation. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000271The chromatic index of a graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000291The number of descents of a binary word. St000295The length of the border of a binary word. St000297The number of leading ones in a binary word. St000304The load of a permutation. St000306The bounce count of a Dyck path. St000310The minimal degree of a vertex of a graph. St000317The cycle descent number 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. St000338The number of pixed points of a permutation. St000355The number of occurrences of the pattern 21-3. St000359The number of occurrences of the pattern 23-1. St000377The dinv defect 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. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000441The number of successions of a permutation. St000442The maximal area to the right of an up step of a Dyck path. St000450The number of edges minus the number of vertices plus 2 of a graph. St000461The rix statistic of a permutation. St000462The major index minus the number of excedences of a permutation. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000475The number of parts equal to 1 in a partition. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000502The number of successions of a set partitions. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000546The number of global descents of a permutation. 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. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000648The number of 2-excedences of a permutation. St000663The number of right floats of a permutation. St000665The number of rafts of a permutation. St000670The reversal length of a permutation. St000672The number of minimal elements in Bruhat order not less than the permutation. St000674The number of hills of a Dyck path. St000682The Grundy value of Welter's game on a binary word. St000683The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000691The number of changes of a binary word. St000731The number of double exceedences of a permutation. St000732The number of double deficiencies of a permutation. St000753The Grundy value for the game of Kayles on a binary word. St000766The number of inversions of an integer composition. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000811The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to Schur symmetric functions. St000837The number of ascents of distance 2 of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000874The position of the last double rise in a Dyck path. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000877The depth of the binary word interpreted as a path. St000878The number of ones minus the number of zeros of a binary word. St000884The number of isolated descents of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St000946The sum of the skew hook positions in a Dyck path. St000948The chromatic discriminant of a graph. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St000984The number of boxes below precisely one peak. St000996The number of exclusive left-to-right maxima of a permutation. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001057The Grundy value of the game of creating an independent set in a graph. St001061The number of indices that are both descents and recoils of a permutation. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001071The beta invariant of the graph. St001084The number of occurrences of the vincular pattern |1-23 in a permutation. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001091The number of parts in an integer partition whose next smaller part has the same size. St001115The number of even descents of a permutation. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001126Number of simple module that are 1-regular in the corresponding Nakayama algebra. St001139The number of occurrences of hills of size 2 in a Dyck path. 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. St001167The number of simple modules that appear as the top of an indecomposable non-projective modules that is reflexive in the corresponding Nakayama algebra. 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. 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 $g$. 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 $eA$. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. 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. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. 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. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001234The number of indecomposable three dimensional modules with projective dimension one. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001249Sum of the odd parts of a partition. St001253The number of non-projective indecomposable reflexive modules in the corresponding Nakayama algebra. St001263The index of the maximal parabolic seaweed algebra associated with the composition. St001274The number of indecomposable injective modules with projective dimension equal to two. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001281The normalized isoperimetric number of a graph. St001287The number of primes obtained by multiplying preimage and image of a permutation and subtracting one. 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. St001298The number of repeated entries in the Lehmer code of a permutation. St001367The smallest number which does not occur as degree of a vertex in a graph. St001375The pancake length of a permutation. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001402The number of separators in a permutation. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001423The number of distinct cubes in a binary word. St001424The number of distinct squares in a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001480The number of simple summands of the module J^2/J^3. St001498The normalised height of a Nakayama algebra with magnitude 1. 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. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001565The number of arithmetic progressions of length 2 in a permutation. St001569The maximal modular displacement of a permutation. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001683The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. 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. St001730The number of times the path corresponding to a binary word crosses the base line. St001760The number of prefix or suffix reversals needed to sort a permutation. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001801Half the number of preimage-image pairs of different parity in a permutation. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001810The number of fixed points of a permutation smaller than its largest moved point. St001811The Castelnuovo-Mumford regularity of a permutation. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001911A descent variant minus the number of inversions. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001948The number of augmented double ascents of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St000007The number of saliances of the permutation. St000013The height of a Dyck path. St000015The number of peaks of a Dyck path. St000026The position of the first return of a Dyck path. St000031The number of cycles in the cycle decomposition of a permutation. St000032The number of elements smaller than the given Dyck path in the Tamari Order. St000054The first entry of the permutation. St000056The decomposition (or block) number of a permutation. St000061The number of nodes on the left branch of a binary tree. St000062The length of the longest increasing subsequence of the 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. St000078The number of alternating sign matrices whose left key is the permutation. St000084The number of subtrees. St000090The variation of a composition. St000133The "bounce" of a permutation. St000146The Andrews-Garvan crank of a partition. St000154The sum of the descent bottoms of a permutation. St000155The number of exceedances (also excedences) of a permutation. St000160The multiplicity of the smallest part of a partition. 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. St000213The number of weak exceedances (also weak excedences) of a permutation. St000216The absolute length of a permutation. St000240The number of indices that are not small excedances. St000255The number of reduced Kogan faces with the permutation as type. St000286The number of connected components of the complement of a graph. St000288The number of ones in a binary word. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000326The position of the first one in a binary word after appending a 1 at the end. St000334The maz index, the major index of a permutation after replacing fixed points by zeros. St000382The first part of an integer composition. St000383The last part of an integer composition. St000414The binary logarithm of the number of binary trees with the same underlying unordered tree. St000420The number of Dyck paths that are weakly above a Dyck path. St000443The number of long tunnels of a Dyck path. St000444The length of the maximal rise of a Dyck path. St000489The number of cycles of a permutation of length at most 3. St000501The size of the first part in the decomposition of a permutation. St000504The cardinality of the first block of a set partition. St000531The leading coefficient of the rook polynomial of an integer partition. St000542The number of left-to-right-minima of a permutation. St000617The number of global maxima of a Dyck path. St000628The balance of a binary word. St000630The length of the shortest palindromic decomposition of a binary word. St000654The first descent of a permutation. St000669The number of permutations obtained by switching ascents or descents of size 2. St000680The Grundy value for Hackendot on posets. St000684The global 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. St000702The number of weak deficiencies of a permutation. St000717The number of ordinal summands of a poset. St000729The minimal arc length of a set partition. St000733The row containing the largest entry 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. St000746The number of pairs with odd minimum in a perfect matching. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000820The number of compositions obtained by rotating the composition. St000823The number of unsplittable factors of the set partition. St000838The number of terminal right-hand endpoints when the vertices are written in order. St000843The decomposition number of a perfect matching. St000876The number of factors in the Catalan decomposition of a binary word. St000883The number of longest increasing subsequences of a permutation. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. St000894The trace of an alternating sign matrix. St000898The number of maximal entries in the last diagonal of the monotone triangle. 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. St000906The length of the shortest maximal chain in a poset. St000908The length of the shortest maximal antichain in a poset. St000909The number of maximal chains of maximal size in a poset. St000910The number of maximal chains of minimal length in a poset. St000914The sum of the values of the Möbius function of a poset. St000971The smallest closer of a set partition. St000982The length of the longest constant subword. St000983The length of the longest alternating subword. St000991The number of right-to-left minima of a permutation. St000993The multiplicity of the largest part of an integer partition. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001007Number of simple modules with projective dimension 1 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. 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. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. 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. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001136The largest label with larger sister in the leaf labelled binary unordered tree associated with the perfect matching. St001187The number of simple modules with grade at least one in the corresponding Nakayama algebra. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001238The number of simple modules S such that the Auslander-Reiten translate of S is isomorphic to the Nakayama functor applied to the second syzygy of S. 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. 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. St001313The number of Dyck paths above the lattice path given by a binary word. St001316The domatic number of a graph. St001372The length of a longest cyclic run of ones of a binary word. St001377The major index minus the number of inversions of a permutation. St001383The BG-rank of an integer partition. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001399The distinguishing number of a poset. St001405The number of bonds in a permutation. St001415The length of the longest palindromic prefix 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. St001461The number of topologically connected components of the chord diagram of a permutation. St001462The number of factors of a standard tableaux under concatenation. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001497The position of the largest weak excedence of a permutation. St001516The number of cyclic bonds of a permutation. St001530The depth of a Dyck path. St001652The length of a longest interval of consecutive numbers. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001660The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board. St001662The length of the longest factor of consecutive numbers in a permutation. St001672The restrained domination number of a graph. St001675The number of parts equal to the part in the reversed composition. St001778The largest greatest common divisor of an element and its image in a permutation. St001806The upper middle entry of a permutation. St001807The lower middle entry of a permutation. St001809The index of the step at the first peak of maximal height in a Dyck path. St001884The number of borders of a binary word. St001933The largest multiplicity of a part in an integer partition. St001959The product of the heights of the peaks of a Dyck path. St000058The order of a permutation. St000144The pyramid weight of the Dyck path. St000289The decimal representation of a binary word. St000485The length of the longest cycle of a permutation. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000738The first entry in the last row of a standard tableau. St000792The Grundy value for the game of ruler on a binary word. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001077The prefix exchange distance of a permutation. St001239The largest vector space dimension of the double dual of a simple module 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. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001566The length of the longest arithmetic progression in a permutation. St000756The sum of the positions of the left to right maxima of a permutation. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001065Number of indecomposable reflexive modules 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 St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St000815The number of semistandard Young tableaux of partition weight of given shape. St000478Another weight of a partition according to Alladi. St000567The sum of the products of all pairs of parts. 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. 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. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000770The major index of an integer partition when read from bottom to top. St000928The sum of the coefficients of the character polynomial of an integer partition. St000933The number of multipartitions of sizes given by an integer partition. St000937The number of positive values of the symmetric group character corresponding to the partition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000438The position of the last up step in a Dyck path. St000327The number of cover relations in a poset. St000493The los statistic of a set partition. St000494The number of inversions of distance at most 3 of a permutation. St000495The number of inversions of distance at most 2 of a permutation. St000498The lcs statistic of a set partition. St000503The maximal difference between two elements in a common block. St000564The number of occurrences of the pattern {{1},{2}} in a set partition. St000577The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element. St000578The number of occurrences of the pattern {{1},{2}} such that 1 is a singleton. St000653The last descent of a permutation. St000693The modular (standard) major index of a standard tableau. St000728The dimension of a set partition. St000730The maximal arc length of a set partition. St000794The mak of a permutation. St000809The reduced reflection length of the permutation. St000831The number of indices that are either descents or recoils. St000833The comajor index of a permutation. St000947The major index east count of a Dyck path. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St001076The minimal length of a factorization of a permutation into transpositions that are cyclic shifts of (12). St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001371The length of the longest Yamanouchi prefix of a binary word. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001721The degree of a binary word. St000082The number of elements smaller than a binary tree in Tamari order. St000280The size of the preimage of the map 'to labelling permutation' from Parking functions to Permutations. St000487The length of the shortest cycle of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St001346The number of parking functions that give the same permutation. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St001500The global dimension of magnitude 1 Nakayama algebras. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001808The box weight or horizontal decoration of a Dyck path. St000219The number of occurrences of the pattern 231 in a permutation. St000354The number of recoils of a permutation. St000391The sum of the positions of the ones in a binary word. St000472The sum of the ascent bottoms of a permutation. St000490The intertwining number of a set partition. St000492The rob statistic of a set partition. St000499The rcb statistic of a set partition. St000539The number of odd inversions of a permutation. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000574The number of occurrences of the pattern {{1},{2}} such that 1 is a minimal and 2 a maximal element. St000579The number of occurrences of the pattern {{1},{2}} such that 2 is a maximal element. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. 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. St000795The mad of a permutation. St000796The stat' of a permutation. St000797The stat`` of a permutation. St000798The makl of a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000849The number of 1/3-balanced pairs in a poset. St000934The 2-degree of an integer partition. St001030Half the number of non-boundary horizontal edges in the fully packed loop corresponding to the alternating sign matrix. St001080The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001645The pebbling number of a connected graph. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St000045The number of linear extensions of a binary tree. St000100The number of linear extensions of a poset. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000488The number of cycles of a permutation of length at most 2. 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. St000925The number of topologically connected components of a set partition. St001062The maximal size of a block of a set partition. St001075The minimal size of a block of a set partition. 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 $eA$. St001534The alternating sum of the coefficients of the Poincare polynomial of the poset cone. St000250The number of blocks (St000105) plus the number of antisingletons (St000248) of a set partition. St000639The number of relations in a poset. St000641The number of non-empty boolean intervals in a poset. St000827The decimal representation of a binary word with a leading 1. St001406The number of nonzero entries in a Gelfand Tsetlin pattern.