St000733The row containing the largest entry of a standard tableau. St000738The first entry in the last row of a standard tableau. St000808The number of up steps of the associated bargraph. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St001330The hat guessing number of a graph. St001733The number of weak left to right maxima of a Dyck path. St001814The number of partitions interlacing the given partition. St000007The number of saliances of the permutation. St000028The number of stack-sorts needed to sort a permutation. St000069The number of maximal elements of a poset. St000245The number of ascents of a permutation. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000378The diagonal inversion number of an integer partition. 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. St000672The number of minimal elements in Bruhat order not less than the permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001090The number of pop-stack-sorts needed to sort a permutation. St001096The size of the overlap set of a permutation. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000655The length of the minimal rise of a Dyck path. St001088Number of indecomposable projective non-injective modules with dominant dimension equal to the injective dimension 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. St000439The position of the first down step of a Dyck path. St000026The position of the first return of a Dyck path. St000383The last part of an integer composition. St000657The smallest part of an integer composition. St000685The dominant dimension of the LNakayama algebra associated to a Dyck path. St000234The number of global ascents of a permutation. St001067The number of simple modules of dominant dimension at least two in the corresponding Nakayama algebra. 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 $c_{n-1}$. St000105The number of blocks in the set partition. St000273The domination number of a graph. St000326The position of the first one in a binary word after appending a 1 at the end. St000363The number of minimal vertex covers of a graph. St000505The biggest entry in the block containing the 1. St000544The cop number of a graph. St000667The greatest common divisor of the parts of the partition. St000700The protection number of an ordered tree. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000775The multiplicity of the largest eigenvalue in a graph. St000839The largest opener of a set partition. 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. St000907The number of maximal antichains of minimal length in a poset. St000916The packing number of a graph. St000971The smallest closer of a set partition. St001009Number of indecomposable injective modules with projective dimension g when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. 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. St001135The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path. St001363The Euler characteristic of a graph according to Knill. St001571The Cartan determinant of the integer partition. St001675The number of parts equal to the part in the reversed composition. St001829The common independence number of a graph. St001933The largest multiplicity of a part in an integer partition. St000546The number of global descents of a permutation. St001176The size of a partition minus its first part. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. 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. St001777The number of weak descents in an integer composition. St000294The number of distinct factors of a binary word. St000518The number of distinct subsequences in a binary word. St000668The least common multiple of the parts of the partition. 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. St001619The number of non-isomorphic sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. 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. St000063The number of linear extensions of a certain poset defined for an integer partition. St000068The number of minimal elements in a poset. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000108The number of partitions contained in the given partition. St000172The Grundy 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. St000444The length of the maximal rise of a Dyck path. St000476The sum of the semi-lengths of tunnels before a valley of a Dyck path. St000532The total number of rook placements on a Ferrers board. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000627The exponent of a binary word. St000675The number of centered multitunnels of a Dyck path. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000722The number of different neighbourhoods in a graph. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000876The number of factors in the Catalan decomposition of a binary word. St000877The depth of the binary word interpreted as a path. St000885The number of critical steps in the Catalan decomposition of a binary word. St000908The length of the shortest maximal antichain in a poset. St000911The number of maximal antichains of maximal size in a poset. St000922The minimal number such that all substrings of this length are unique. St000932The number of occurrences of the pattern UDU in a Dyck path. St000982The length of the longest constant subword. St001029The size of the core of a graph. St001052The length of the exterior of a permutation. St001068Number of torsionless simple modules 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. 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. 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. St001389The number of partitions of the same length below the given integer 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. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001616The number of neutral elements in a lattice. St001670The connected partition number of a graph. St001720The minimal length of a chain of small intervals in a lattice. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001883The mutual visibility number of a graph. St001884The number of borders of a binary word. St000008The major index of the composition. St000012The area of a Dyck path. St000053The number of valleys of the Dyck path. St000148The number of odd parts of a partition. St000171The degree of the graph. St000211The rank of the set partition. St000228The size of a partition. St000272The treewidth of a graph. St000295The length of the border of a binary word. St000362The size of a minimal vertex cover of a graph. St000369The dinv deficit of a Dyck path. St000376The bounce deficit of a Dyck path. St000384The maximal part of the shifted composition of an integer partition. 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. St000454The largest eigenvalue of a graph if it is integral. St000459The hook length of the base cell of a partition. St000475The number of parts equal to 1 in a partition. St000519The largest length of a factor maximising the subword complexity. St000536The pathwidth 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. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001091The number of parts in an integer partition whose next smaller part has the same size. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001127The sum of the squares of the parts of a partition. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001622The number of join-irreducible elements of a lattice. St001644The dimension of a graph. St001826The maximal number of leaves on a vertex of a graph. St001075The minimal size of a block of a set partition. St000501The size of the first part in the decomposition of a permutation. St000504The cardinality of the first block of a set partition. St000542The number of left-to-right-minima of a permutation. St000678The number of up steps after the last double rise of a Dyck path. St000729The minimal arc length of a set partition. St000823The number of unsplittable factors of the set partition. St000925The number of topologically connected components of a set partition. St000993The multiplicity of the largest part of an integer partition. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St000210Minimum over maximum difference of elements in cycles. St000502The number of successions of a set partitions. St000864The number of circled entries of the shifted recording tableau of a permutation. St001357The maximal degree of a regular spanning subgraph of a graph. St001371The length of the longest Yamanouchi prefix of a binary word. St000617The number of global maxima of a Dyck path. St000306The bounce count of a Dyck path. St000553The number of blocks of a graph. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000708The product of the parts of an integer partition. St000730The maximal arc length of a set partition. St000770The major index of an integer partition when read from bottom to top. St000909The number of maximal chains of maximal size in a poset. St000914The sum of the values of the Möbius function of a poset. St001062The maximal size of a block of a set partition. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001313The number of Dyck paths above the lattice path given by a binary word. St001316The domatic number of a graph. St001725The harmonious chromatic number of a graph. St001963The tree-depth of a graph. St000247The number of singleton blocks of a set partition. St000441The number of successions of a permutation. St000491The number of inversions of a set partition. St000493The los statistic of a set partition. St000497The lcb statistic of a set partition. St000498The lcs statistic of a set partition. St000503The maximal difference between two elements in a common block. St000555The number of occurrences of the pattern {{1,3},{2}} in a set partition. St000564The number of occurrences of the pattern {{1},{2}} in a set partition. St000567The sum of the products of all pairs of parts. St000572The dimension exponent of 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. St000581The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 2 is maximal. St000582The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, 3 is maximal, (1,3) are consecutive in a block. 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. St000600The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal, (1,3) are consecutive in a block. St000602The number of occurrences of the pattern {{1,3},{2}} such that 1 is minimal. 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. St000682The Grundy value of Welter's game on a binary word. St000728The dimension of a set partition. St000874The position of the last double rise in a Dyck path. St000984The number of boxes below precisely one peak. 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. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001358The largest degree of a regular subgraph of a graph. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001962The proper pathwidth of a graph. St000487The length of the shortest cycle of a permutation. St000990The first ascent 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. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000529The number of permutations whose descent word is the given binary word. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000717The number of ordinal summands of a poset. St001498The normalised height of a Nakayama algebra with magnitude 1. St000293The number of inversions of a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St000906The length of the shortest maximal chain in a poset. St000214The number of adjacencies of a permutation. St000590The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 1 is maximal, (2,3) are consecutive in a block. St000873The aix statistic of a permutation. St000931The number of occurrences of the pattern UUU in a Dyck path. St000883The number of longest increasing subsequences of a permutation. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000989The number of final rises of a permutation. St001061The number of indices that are both descents and recoils of a permutation. St000456The monochromatic index of a connected graph. St000661The number of rises of length 3 of a Dyck path. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001141The number of occurrences of hills of size 3 in a Dyck path. St000203The number of external nodes of a binary tree. St000409The number of pitchforks in a binary tree. St000618The number of self-evacuating tableaux of given shape. St000674The number of hills of a Dyck path. St000701The protection number of a binary tree. St000781The number of proper colouring schemes of a Ferrers diagram. St000838The number of terminal right-hand endpoints when the vertices are written in order. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001063Numbers of 3-torsionfree simple modules in the corresponding Nakayama algebra. St001064Number of simple modules in the corresponding Nakayama algebra that are 3-syzygy modules. St001066The number of simple reflexive modules in the corresponding Nakayama algebra. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001432The order dimension of the partition. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. St001483The number of simple module modules that appear in the socle of the regular module but have no nontrivial selfextensions with the regular module. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001562The value of the complete homogeneous symmetric function evaluated at 1. St001563The value of the power-sum symmetric function evaluated at 1. St001564The value of the forgotten symmetric functions when all variables set to 1. St001592The maximal number of simple paths between any two different vertices of a graph. St001593This is the number of standard Young tableaux of the given shifted shape. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001780The order of promotion on the set of standard tableaux of given shape. St001786The number of total orderings of the north steps of a Dyck path such that steps after the k-th east step are not among the first k positions in the order. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St000118The number of occurrences of the contiguous pattern [.,[.,[.,.]]] in a binary tree. St000121The number of occurrences of the contiguous pattern [.,[.,[.,[.,.]]]] in a binary tree. St000122The number of occurrences of the contiguous pattern [.,[.,[[.,.],.]]] in a binary tree. St000125The number of occurrences of the contiguous pattern [.,[[[.,.],.],. St000126The number of occurrences of the contiguous pattern [.,[.,[.,[.,[.,.]]]]] in a binary tree. St000127The number of occurrences of the contiguous pattern [.,[.,[.,[[.,.],.]]]] in a binary tree. St000128The number of occurrences of the contiguous pattern [.,[.,[[.,[.,.]],.]]] in a binary tree. St000129The number of occurrences of the contiguous pattern [.,[.,[[[.,.],.],.]]] in a binary tree. St000130The number of occurrences of the contiguous pattern [.,[[.,.],[[.,.],.]]] in a binary tree. St000131The number of occurrences of the contiguous pattern [.,[[[[.,.],.],.],. St000132The number of occurrences of the contiguous pattern [[.,.],[.,[[.,.],.]]] in a binary tree. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000232The number of crossings of a set partition. St000379The number of Hamiltonian cycles in a graph. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000559The number of occurrences of the pattern {{1,3},{2,4}} in a set partition. St000561The number of occurrences of the pattern {{1,2,3}} in a set partition. St000563The number of overlapping pairs of blocks of a set partition. St000660The number of rises of length at least 3 of a Dyck path. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St000699The toughness times the least common multiple of 1,. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000944The 3-degree of an integer partition. St000966Number of peaks minus the global dimension of the corresponding LNakayama algebra. St000974The length of the trunk of an ordered tree. St001025Number of simple modules with projective dimension 4 in the Nakayama algebra corresponding to the Dyck path. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001137Number of simple modules that are 3-regular in the corresponding Nakayama algebra. St001172The number of 1-rises at odd height of a Dyck path. St001175The size of a partition minus the hook length of the base cell. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001584The area statistic between a Dyck path and its bounce path. St001586The number of odd parts smaller than the largest even part in an integer partition. St001657The number of twos in an integer partition. St001696The natural major index of a standard Young tableau. St001932The number of pairs of singleton blocks in the noncrossing set partition corresponding to a Dyck path, that can be merged to create another noncrossing set partition. St001961The sum of the greatest common divisors of all pairs of parts. St000066The column of the unique '1' in the first row of the alternating sign matrix. St001652The length of a longest interval of consecutive numbers. St001662The length of the longest factor of consecutive numbers in a permutation. St000237The number of small exceedances. St001640The number of ascent tops in the permutation such that all smaller elements appear before. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St000264The girth of a graph, which is not a tree. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. 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 $eA$. St001568The smallest positive integer that does not appear twice in the partition. St001159Number of simple modules with dominant dimension equal to the global dimension in the corresponding Nakayama algebra. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001800The number of 3-Catalan paths having this Dyck path as first and last coordinate projections. St000478Another weight of a partition according to Alladi. St000629The defect of a binary word. St000929The constant term of the character polynomial of an integer partition. St001193The dimension of $Ext_A^1(A/AeA,A)$ in the corresponding Nakayama algebra $A$ such that $eA$ is a minimal faithful projective-injective module. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. 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. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St000842The breadth of a permutation. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St001399The distinguishing number of a poset. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001248Sum of the even parts of a partition. St001394The genus of a permutation. St001587Half of the largest even part of an integer partition. St000451The length of the longest pattern of the form k 1 2. St000910The number of maximal chains of minimal length in a poset. St001162The minimum jump of a permutation. St001344The neighbouring number of a permutation. St000358The number of occurrences of the pattern 31-2. St000360The number of occurrences of the pattern 32-1. St000367The number of simsun double descents of a permutation. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000406The number of occurrences of the pattern 3241 in a permutation. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000623The number of occurrences of the pattern 52341 in a permutation. St000649The number of 3-excedences of a permutation. St000709The number of occurrences of 14-2-3 or 14-3-2. St000732The number of double deficiencies of a permutation. St000750The number of occurrences of the pattern 4213 in a permutation. St000801The number of occurrences of the vincular pattern |312 in a permutation. St000802The number of occurrences of the vincular pattern |321 in a permutation. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St000962The 3-shifted major index of a permutation. St001411The number of patterns 321 or 3412 in a permutation. St001513The number of nested exceedences of a permutation. St001537The number of cyclic crossings of a permutation. St001549The number of restricted non-inversions between exceedances. St001550The number of inversions between exceedances where the greater exceedance is linked. St001551The number of restricted non-inversions between exceedances where the rightmost exceedance is linked. St001552The number of inversions between excedances and fixed points of a permutation. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. St001715The number of non-records in a permutation. St001728The number of invisible descents of a permutation. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001847The number of occurrences of the pattern 1432 in a permutation. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St000374The number of exclusive right-to-left minima of a permutation. St000527The width of the poset. St000725The smallest label of a leaf of the increasing binary tree associated to a permutation. St001722The number of minimal chains with small intervals between a binary word and the top element. St001461The number of topologically connected components of the chord diagram of a permutation. St001332The number of steps on the non-negative side of the walk associated with the permutation. St000740The last entry of a permutation. St001631The number of simple modules $S$ with $dim Ext^1(S,A)=1$ in the incidence algebra $A$ of the poset. St000145The Dyson rank of a partition. St000058The order of a permutation. St000258The burning number of a graph. 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. St000734The last entry in the first row of a standard tableau. St000918The 2-limited packing number of a graph. St000284The Plancherel distribution on integer partitions. St000308The height of the tree associated to a permutation. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000706The product of the factorials of the multiplicities of an integer partition. St000805The number of peaks of the associated bargraph. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000934The 2-degree of an integer partition. St000946The sum of the skew hook positions in a Dyck path. 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. St001012Number of simple modules with projective dimension at most 2 in 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. 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. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001128The exponens consonantiae of a partition. St001166Number of indecomposable projective non-injective modules with dominant dimension equal to the global dimension plus the number of indecomposable projective injective modules in the corresponding Nakayama algebra. St001340The cardinality of a minimal non-edge isolating set of a graph. St001778The largest greatest common divisor of an element and its image in a permutation. St001958The degree of the polynomial interpolating the values of a permutation. St000455The second largest eigenvalue of a graph if it is integral. St000807The sum of the heights of the valleys of the associated bargraph. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St000941The number of characters of the symmetric group whose value on the partition is even. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001098The 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 vertex labelled trees. 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. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. 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. St001298The number of repeated entries in the Lehmer code 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. 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. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St000056The decomposition (or block) number of a permutation. St000654The first descent of a permutation. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. 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. St001481The minimal height of a peak of a Dyck path. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001274The number of indecomposable injective modules with projective dimension equal to two. St000084The number of subtrees. St000287The number of connected components of a graph. St000314The number of left-to-right-maxima of a permutation. St000335The difference of lower and upper interactions. St000843The decomposition number of a perfect matching. 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. 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 $g$. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001828The Euler characteristic of a graph. St000051The size of the left subtree of a binary tree. St001130The number of two successive successions in a permutation. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St000015The number of peaks of a Dyck path. 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. St000286The number of connected components of the complement of a graph. St000352The Elizalde-Pak rank of a permutation. St000420The number of Dyck paths that are weakly above a Dyck path. St000702The number of weak deficiencies of a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000822The Hadwiger number of the graph. St000887The maximal number of nonzero entries on a diagonal of a permutation matrix. 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. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001530The depth of a Dyck path. St000090The variation of a composition. St000133The "bounce" of a permutation. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. 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. St000419The number of Dyck paths that are weakly above the Dyck path, except for the path itself. St000961The shifted major index 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. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001205The number of non-simple indecomposable projective-injective modules of the algebra $eAe$ in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. 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. 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. 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. St000061The number of nodes on the left branch of a binary tree. St000485The length of the longest cycle of a permutation. St001133The smallest label in the subtree rooted at the sister of 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001134The largest label in the subtree rooted at the sister of 1 in the leaf labelled binary unordered tree associated with the perfect matching. St000530The number of permutations with the same descent word as the given permutation. St000619The number of cyclic descents of a permutation. St000652The maximal difference between successive positions of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000988The orbit size of a permutation under Foata's bijection. St001246The maximal difference between two consecutive entries of a permutation. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St000354The number of recoils of a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000538The number of even inversions of a permutation. St000539The number of odd inversions of a permutation. St000653The last descent of a permutation. St000711The number of big exceedences of a permutation. St000794The mak of a permutation. St000795The mad of a permutation. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000829The Ulam distance of a permutation to the identity permutation. St000831The number of indices that are either descents or recoils. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St000956The maximal displacement of a permutation. St000957The number of Bruhat lower covers of a permutation. St001480The number of simple summands of the module J^2/J^3. St001812The biclique partition number of a graph. St000036The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation. St000119The number of occurrences of the pattern 321 in a permutation. St000359The number of occurrences of the pattern 23-1. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001545The second Elser number of a connected graph. St000648The number of 2-excedences of a permutation. St001132The number of leaves in the subtree whose sister has label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001060The distinguishing index of a graph. St000260The radius of a connected graph. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St000047The number of standard immaculate tableaux of a given shape. St000079The number of alternating sign matrices for a given Dyck path. St000255The number of reduced Kogan faces with the permutation as type. St000570The Edelman-Greene number of a permutation. St000694The number of affine bounded permutations that project to a given permutation. St000760The length of the longest strictly decreasing subsequence of parts of an integer composition. St000832The number of permutations obtained by reversing blocks of three consecutive numbers. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000889The number of alternating sign matrices with the same antidiagonal sums. St000968We 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 $c_{n−1}$. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001204Call 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. 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. St001256Number of simple reflexive modules that are 2-stable reflexive. St001289The vector space dimension of the n-fold tensor product of D(A), where n is maximal such that this n-fold tensor product is nonzero. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001941The evaluation at 1 of the modified Kazhdan--Lusztig R polynomial (as in [1, Section 5. St000042The number of crossings of a perfect matching. St000221The number of strong fixed points of a permutation. St000279The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations. St000317The cycle descent number of a permutation. St000365The number of double ascents of a permutation. St000407The number of occurrences of the pattern 2143 in a permutation. St000650The number of 3-rises of a permutation. St000664The number of right ropes of a permutation. St000666The number of right tethers of a permutation. St000766The number of inversions of an integer composition. St000768The number of peaks in an integer composition. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000878The number of ones minus the number of zeros of a binary word. St000879The number of long braid edges in the graph of braid moves of a permutation. 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. St001047The maximal number of arcs crossing a given arc of a perfect matching. St001059Number of occurrences of the patterns 41352,42351,51342,52341 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. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001139The number of occurrences of hills of size 2 in a Dyck path. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. 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. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001381The fertility of a permutation. St001663The number of occurrences of the Hertzsprung pattern 132 in a permutation. 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. St001766The number of cells which are not occupied by the same tile in all reduced pipe dreams corresponding to a permutation. St001810The number of fixed points of a permutation smaller than its largest moved point. St000464The Schultz index of a connected graph. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001118The acyclic chromatic index of a graph. St001281The normalized isoperimetric number of a graph. St000800The number of occurrences of the vincular pattern |231 in a permutation. St000630The length of the shortest palindromic decomposition of a binary word. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001471The magnitude of a Dyck path. St001497The position of the largest weak excedence of a permutation. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000913The number of ways to refine the partition into singletons. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. St001188The number of simple modules $S$ with grade $\inf \{ i \geq 0 | Ext^i(S,A) \neq 0 \}$ at least two in the Nakayama algebra $A$ corresponding to the Dyck path. St001196The global dimension of $A$ minus the global dimension of $eAe$ for the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001385The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001613The binary logarithm of the size of the center of a lattice. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001881The number of factors of a lattice as a Cartesian product of lattices. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St001181Number of indecomposable injective modules with grade at least 3 in the corresponding Nakayama algebra. St001588The number of distinct odd parts smaller than the largest even part in an integer partition. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St000144The pyramid weight of the Dyck path. St000213The number of weak exceedances (also weak excedences) of a permutation. St000236The number of cyclical small weak excedances. St000628The balance of a binary word. St000724The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St000731The number of double exceedences of a permutation. St000924The number of topologically connected components of a perfect matching. St001081The number of minimal length factorizations of a permutation into star transpositions. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000837The number of ascents of distance 2 of a permutation. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001082The number of boxed occurrences of 123 in a permutation. St001249Sum of the odd parts of a partition. St001283The number of finite solvable groups that are realised by the given partition over the complex numbers. St001284The number of finite groups that are realised by the given partition over the complex numbers. St001383The BG-rank of an integer partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. 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. St001346The number of parking functions that give the same 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. St000888The maximal sum of entries on a diagonal of an alternating sign matrix. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001959The product of the heights of the peaks of a Dyck path. St000083The number of left oriented leafs of a binary tree except the first one. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000461The rix statistic of a permutation. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001730The number of times the path corresponding to a binary word crosses the base line. St001948The number of augmented double ascents of a permutation. St000477The weight of a partition according to Alladi. St000045The number of linear extensions of a binary tree. St000898The number of maximal entries in the last diagonal of the monotone triangle. St000788The number of nesting-similar perfect matchings of a perfect matching. St001487The number of inner corners of a skew partition. St001490The number of connected components of a skew partition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001890The maximum magnitude of the Möbius function of a poset. St000787The number of flips required to make a perfect matching noncrossing. St001095The number of non-isomorphic posets with precisely one further covering relation. St001435The number of missing boxes in the first row. St001438The number of missing boxes of a skew partition. St001651The Frankl number of a lattice. St000115The single entry in the last row. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St001591The number of graphs with the given composition of multiplicities of Laplacian eigenvalues. St001732The number of peaks visible from the left. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. St001889The size of the connectivity set of a signed permutation. St000402Half the size of the symmetry class of a permutation. St001200The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St000338The number of pixed points of a permutation. St000486The number of cycles of length at least 3 of a permutation. St000710The number of big deficiencies of a permutation. St000764The number of strong records in an integer composition. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000892The maximal number of nonzero entries on a diagonal of an alternating sign matrix. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. 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 $K[x]/(x^n)$. St001468The smallest fixpoint of a permutation. St001590The crossing number of a perfect matching. St001830The chord expansion number of a perfect matching. St001832The number of non-crossing perfect matchings in the chord expansion of a perfect matching. St000488The number of cycles of a permutation of length at most 2. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St000894The trace of an alternating sign matrix. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001444The rank of the skew-symmetric form which is non-zero on crossing arcs of a perfect matching. St001520The number of strict 3-descents. St001811The Castelnuovo-Mumford regularity of a permutation. St001837The number of occurrences of a 312 pattern in the restricted growth word of a perfect matching. St001856The number of edges in the reduced word graph of a permutation. St001904The length of the initial strictly increasing segment of a parking function. St001937The size of the center of a parking function. St001557The number of inversions of the second entry of a permutation. 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. St000253The crossing number of a set partition. St000659The number of rises of length at least 2 of a Dyck path. St000763The sum of the positions of the strong records of an integer composition. St000942The number of critical left to right maxima of the parking functions. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000215The number of adjacencies of a permutation, zero appended. St000560The number of occurrences of the pattern {{1,2},{3,4}} in a set partition. St000562The number of internal points of a set partition. St000761The number of ascents in an integer composition. St000769The major index of a composition regarded as a word. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St001087The number of occurrences of the vincular pattern |12-3 in a permutation. St001413Half the length of the longest even length palindromic prefix of a binary word. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001960The number of descents of a permutation minus one if its first entry is not one. St001273The projective dimension of the first term in an injective coresolution of the regular module. St000252The number of nodes of degree 3 of a binary tree. St000366The number of double descents of a permutation. St000751The number of occurrences of either of the pattern 2143 or 2143 in a permutation. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St000937The number of positive values of the symmetric group character corresponding to the partition. St000997The even-odd crank of an integer partition. St001555The order of a signed permutation. St000681The Grundy value of Chomp on Ferrers diagrams. St000762The sum of the positions of the weak records of an integer composition. St000939The number of characters of the symmetric group whose value on the partition is positive. St000508Eigenvalues of the random-to-random operator acting on a simple module. St000509The diagonal index (content) of a partition. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000928The sum of the coefficients of the character polynomial of an integer partition. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000933The number of multipartitions of sizes given by an integer partition. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000707The product of the factorials of the parts. St000815The number of semistandard Young tableaux of partition weight of given shape. St000927The alternating sum of the coefficients of the character polynomial of an integer partition. St000716The dimension of the irreducible representation of Sp(6) labelled by an integer partition. St000886The number of permutations with the same antidiagonal sums. 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. St000756The sum of the positions of the left to right maxima of a permutation. St000779The tier of a permutation. St001043The depth of the leaf closest to the root in the binary unordered tree associated with the perfect matching. St001045The number of leaves in the subtree not containing one in the decreasing labelled binary unordered tree associated with the perfect matching. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001645The pebbling number of a connected graph. St001735The number of permutations with the same set of runs. St001896The number of right descents of a signed permutations. St001905The number of preferred parking spots in a parking function less than the index of the car. St000089The absolute variation of a composition. St000091The descent variation of a composition. St000233The number of nestings of a set partition. St000355The number of occurrences of the pattern 21-3. St000425The number of occurrences of the pattern 132 or of the pattern 213 in a permutation. St000496The rcs statistic of a set partition. St000583The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 1, 2 are maximal. St000663The number of right floats of a permutation. St001301The first Betti number of the order complex associated with the poset. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001535The number of cyclic alignments of a permutation. St001536The number of cyclic misalignments of a permutation. St001687The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation. St001781The interlacing number of a set partition. St001839The number of excedances of a set partition. St001840The number of descents of a set partition. St001841The number of inversions of a set partition. St001842The major index of a set partition. St001843The Z-index of a set partition. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001816Eigenvalues of the top-to-random operator acting on a simple module. St000469The distinguishing number of a graph. St000806The semiperimeter of the associated bargraph. St000896The number of zeros on the main diagonal of an alternating sign matrix. St000230Sum of the minimal elements of the blocks of a set partition. St000492The rob statistic of a set partition. St001207The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001665The number of pure excedances of a permutation. St001737The number of descents of type 2 in a permutation. 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. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St001247The number of parts of a partition that are not congruent 2 modulo 3. 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. St001795The binary logarithm of the evaluation of the Tutte polynomial of the graph at (x,y) equal to (-1,-1). St001964The interval resolution global dimension of a poset. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001875The number of simple modules with projective dimension at most 1. St000254The nesting number of a set partition. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000516The number of stretching pairs of a permutation. St000565The major index of a set partition. St000596The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 1 is maximal. St000646The number of big ascents of a permutation. St000748The major index of the permutation obtained by flattening the set partition. St001423The number of distinct cubes in a binary word. St001556The number of inversions of the third entry of a permutation. St001280The number of parts of an integer partition that are at least two. St000075The orbit size of a standard tableau under promotion. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000166The depth minus 1 of an ordered tree. St000522The number of 1-protected nodes of a rooted tree. St000893The number of distinct diagonal sums of an alternating sign matrix. St001114The number of odd descents of a permutation. St001637The number of (upper) dissectors of a poset. St001773The number of minimal elements in Bruhat order not less than the signed permutation. St001863The number of weak excedances of a signed permutation. St001864The number of excedances of a signed permutation. St001928The number of non-overlapping descents in a permutation. St000071The number of maximal chains in a poset. St000094The depth of an ordered tree. St000100The number of linear extensions of a poset. St000174The flush statistic of a semistandard tableau. St000521The number of distinct subtrees of an ordered tree. St000589The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block. St000880The number of connected components of long braid edges in the graph of braid moves of a permutation. St000923The minimal number with no two order isomorphic substrings of this length in a permutation. St000973The length of the boundary of an ordered tree. St000975The length of the boundary minus the length of the trunk of an ordered tree. 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. St001566The length of the longest arithmetic progression in a permutation. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001820The size of the image of the pop stack sorting operator. St001862The number of crossings of a signed permutation. St001935The number of ascents in a parking function. St000881The number of short braid edges in the graph of braid moves of a permutation. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001846The number of elements which do not have a complement in the lattice. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000474Dyson's crank of a partition. St001527The cyclic permutation representation number of an integer partition.