St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St001029The size of the core of a graph. St001109The number of proper colourings of a graph with as few colours as possible. St001316The domatic number of a graph. St001330The hat guessing number of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St000439The position of the first down step of a Dyck path. St000234The number of global ascents of a permutation. St000245The number of ascents of a permutation. St000260The radius of a connected graph. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St000672The number of minimal elements in Bruhat order not less than the permutation. St000834The number of right outer peaks of a permutation. St000846The maximal number of elements covering an element of a poset. St001092The number of distinct even parts of a partition. St001096The size of the overlap set of a permutation. St001280The number of parts of an integer partition that are at least two. St001335The cardinality of a minimal cycle-isolating set of a graph. St001395The number of strictly unfriendly partitions of a graph. St001587Half of the largest even part of an integer partition. St001613The binary logarithm of the size of the center of a lattice. St001777The number of weak descents in an integer composition. St001826The maximal number of leaves on a vertex of a graph. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001931The weak major index of an integer composition regarded as a word. St000010The length of the partition. St000011The number of touch points (or returns) of a Dyck path. St000013The height of a Dyck path. St000058The order of a permutation. St000093The cardinality of a maximal independent set of vertices of a graph. St000147The largest part of an integer partition. St000153The number of adjacent cycles of a permutation. St000258The burning number of a graph. St000273The domination number of a graph. St000346The number of coarsenings of a partition. St000382The first part of an integer composition. St000396The register function (or Horton-Strahler number) of a binary tree. St000397The Strahler number of a rooted tree. St000701The protection number of a binary tree. St000738The first entry in the last row of a standard tableau. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000971The smallest closer of a set partition. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001486The number of corners of the ribbon associated with an integer composition. St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition. St001809The index of the step at the first peak of maximal height in a Dyck path. St001829The common independence number of a graph. 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. St000456The monochromatic index of a connected graph. St000504The cardinality of the first block of a set partition. St000678The number of up steps after the last double rise of a Dyck path. St000695The number of blocks in the first part of the atomic decomposition of a set partition. St000823The number of unsplittable factors of the set partition. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001075The minimal size of a block of a set partition. St001501The dominant dimension of magnitude 1 Nakayama algebras. St001592The maximal number of simple paths between any two different vertices of a graph. St000379The number of Hamiltonian cycles in a graph. St000559The number of occurrences of the pattern {{1,3},{2,4}} in a set partition. St000563The number of overlapping pairs of blocks of a set partition. St000674The number of hills of a Dyck path. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001139The number of occurrences of hills of size 2 in a Dyck path. St001141The number of occurrences of hills of size 3 in a Dyck path. St000026The position of the first return of a Dyck path. St000036The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation. St000054The first entry of the permutation. St000056The decomposition (or block) number of a permutation. St000253The crossing number of a set partition. St000254The nesting number of a set partition. St000255The number of reduced Kogan faces with the permutation as type. St000285The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions. St000297The number of leading ones in a binary word. St000326The position of the first one in a binary word after appending a 1 at the end. St000392The length of the longest run of ones in a binary word. St000442The maximal area to the right of an up step of a Dyck path. St000487The length of the shortest cycle of a permutation. St000501The size of the first part in the decomposition of a permutation. St000529The number of permutations whose descent word is the given binary word. St000542The number of left-to-right-minima of a permutation. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000630The length of the shortest palindromic decomposition of a binary word. St000655The length of the minimal rise of a Dyck path. St000659The number of rises of length at least 2 of a Dyck path. St000675The number of centered multitunnels of a Dyck path. St000706The product of the factorials of the multiplicities of an integer partition. St000729The minimal arc length of a set partition. St000740The last entry of a permutation. St000762The sum of the positions of the weak records of an integer composition. St000847The number of standard Young tableaux whose descent set is the binary word. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000919The number of maximal left branches of a binary tree. St000983The length of the longest alternating subword. St000990The first ascent of a permutation. St000991The number of right-to-left minima of a permutation. St000993The multiplicity of the largest part of an integer partition. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001052The length of the exterior of a permutation. St001162The minimum jump of a permutation. St001313The number of Dyck paths above the lattice path given by a binary word. St001344The neighbouring number of a permutation. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001468The smallest fixpoint of a permutation. St001568The smallest positive integer that does not appear twice in the partition. St001722The number of minimal chains with small intervals between a binary word and the top element. St001838The number of nonempty primitive factors of a binary word. St000119The number of occurrences of the pattern 321 in a permutation. St000133The "bounce" of a permutation. St000210Minimum over maximum difference of elements in cycles. St000288The number of ones in a binary word. St000289The decimal representation of a binary word. St000290The major index of a binary word. St000291The number of descents of a binary word. St000292The number of ascents of a binary word. St000293The number of inversions of a binary word. St000347The inversion sum of a binary word. St000348The non-inversion sum of a binary word. St000352The Elizalde-Pak rank 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 $3$. St000389The number of runs of ones of odd length in a binary word. St000390The number of runs of ones in a binary word. St000391The sum of the positions of the ones in a binary word. St000406The number of occurrences of the pattern 3241 in a permutation. St000407The number of occurrences of the pattern 2143 in a permutation. St000444The length of the maximal rise of a Dyck path. St000478Another weight of a partition according to Alladi. St000491The number of inversions of a set partition. St000497The lcb statistic of a set partition. St000502The number of successions of a set partitions. St000508Eigenvalues of the random-to-random operator acting on a simple module. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000555The number of occurrences of the pattern {{1,3},{2}} in a set partition. St000562The number of internal points of a set partition. St000565The major index of a set partition. St000572The dimension exponent of a set partition. 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. 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. 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. St000623The number of occurrences of the pattern 52341 in a permutation. St000628The balance of a binary word. St000629The defect of a binary word. St000658The number of rises of length 2 of a Dyck path. St000661The number of rises of length 3 of a Dyck path. St000668The least common multiple of the parts of the partition. St000682The Grundy value of Welter's game on a binary word. St000691The number of changes of a binary word. St000699The toughness times the least common multiple of 1,. St000748The major index of the permutation obtained by flattening the set partition. St000750The number of occurrences of the pattern 4213 in a permutation. St000753The Grundy value for the game of Kayles on a binary word. 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. St000792The Grundy value for the game of ruler on a binary word. St000799The number of occurrences of the vincular pattern |213 in a permutation. St000800The number of occurrences of the vincular pattern |231 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. St000842The breadth of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000879The number of long braid edges in the graph of braid moves of a permutation. St000921The number of internal inversions of a binary word. St000929The constant term of the character polynomial of an integer partition. St000931The number of occurrences of the pattern UUU in a Dyck path. St000932The number of occurrences of the pattern UDU in a Dyck path. St000961The shifted major index of a permutation. St001059Number of occurrences of the patterns 41352,42351,51342,52341 in a permutation. St001281The normalized isoperimetric number of a graph. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001371The length of the longest Yamanouchi prefix of a binary word. St001372The length of a longest cyclic run of ones of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001485The modular major index of a binary word. St001513The number of nested exceedences of a permutation. St001550The number of inversions between exceedances where the greater exceedance is linked. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. St001640The number of ascent tops in the permutation such that all smaller elements appear before. 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. St001715The number of non-records in a permutation. St001728The number of invisible descents of a permutation. St001730The number of times the path corresponding to a binary word crosses the base line. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St001766The number of cells which are not occupied by the same tile in all reduced pipe dreams corresponding to a permutation. St001847The number of occurrences of the pattern 1432 in a permutation. St000570The Edelman-Greene number of a permutation. St000667The greatest common divisor of the parts of the partition. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001859The number of factors of the Stanley symmetric function associated with a permutation. St000279The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations. St000516The number of stretching pairs of a permutation. St000622The number of occurrences of the patterns 2143 or 4231 in a permutation. St000709The number of occurrences of 14-2-3 or 14-3-2. St000732The number of double deficiencies of a permutation. St000803The number of occurrences of the vincular pattern |132 in a permutation. St000873The aix statistic of a permutation. St000918The 2-limited packing number of a graph. St000989The number of final rises of a permutation. St001552The number of inversions between excedances and fixed points of a permutation. St000886The number of permutations with the same antidiagonal sums. St001333The cardinality of a minimal edge-isolating set of a graph. St001393The induced matching number of a graph. St000432The number of occurrences of the pattern 231 or of the pattern 312 in a permutation. St000436The number of occurrences of the pattern 231 or of the pattern 321 in a permutation. St000486The number of cycles of length at least 3 of a permutation. St000710The number of big deficiencies of a permutation. St000779The tier of a permutation. St000872The number of very big descents of a permutation. St000962The 3-shifted major index of a permutation. St000963The 2-shifted major index of a permutation. St001261The Castelnuovo-Mumford regularity of a graph. St001498The normalised height of a Nakayama algebra with magnitude 1. St000264The girth of a graph, which is not a tree. St001340The cardinality of a minimal non-edge isolating set of a graph. St001593This is the number of standard Young tableaux of the given shifted shape. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St000298The order dimension or Dushnik-Miller dimension of a poset. St000642The size of the smallest orbit of antichains under Panyushev complementation. 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. St000069The number of maximal elements of a poset. St000717The number of ordinal summands of a poset. St000906The length of the shortest maximal chain in a poset. 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. St000451The length of the longest pattern of the form k 1 2. St000914The sum of the values of the Möbius function of a poset. St000527The width of the poset. St000374The number of exclusive right-to-left minima of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St001004The number of indices that are either left-to-right maxima or right-to-left minima. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000751The number of occurrences of either of the pattern 2143 or 2143 in a permutation. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St000640The rank of the largest boolean interval in a poset. St000455The second largest eigenvalue of a graph if it is integral. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000822The Hadwiger number of the graph. St001060The distinguishing index of a graph. St000068The number of minimal elements in a poset. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000296The length of the symmetric border of a binary word. St000007The number of saliances of the permutation. St000141The maximum drop size of a permutation. St000662The staircase size of the code of a permutation. St000473The number of parts of a partition that are strictly bigger than the number of ones. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000741The Colin de Verdière graph invariant. St000028The number of stack-sorts needed to sort a permutation. St000862The number of parts of the shifted shape of a permutation. St000742The number of big ascents of a permutation after prepending zero. St000066The column of the unique '1' in the first row of the alternating sign matrix. St001111The weak 2-dynamic chromatic number of a graph. St001716The 1-improper chromatic number of a graph. St001108The 2-dynamic chromatic number of a graph. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St000051The size of the left subtree of a binary tree. St000091The descent variation of a composition. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000183The side length of the Durfee square of an integer partition. St000552The number of cut vertices of a graph. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000761The number of ascents in an integer composition. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001214The aft of an integer partition. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001298The number of repeated entries in the Lehmer code of a permutation. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001665The number of pure excedances of a permutation. St001689The number of celebrities in a graph. St001692The number of vertices with higher degree than the average degree in a graph. St001737The number of descents of type 2 in a permutation. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001803The maximal overlap of the cylindrical tableau associated with a tableau. 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. St000062The length of the longest increasing subsequence of the permutation. St000084The number of subtrees. St000159The number of distinct parts of the integer partition. St000236The number of cyclical small weak excedances. St000239The number of small weak excedances. St000259The diameter of a connected graph. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000308The height of the tree associated to a permutation. St000314The number of left-to-right-maxima of a permutation. St000351The determinant of the adjacency matrix of a graph. St000378The diagonal inversion number of an integer partition. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000536The pathwidth of a graph. St000544The cop number of a graph. St000549The number of odd partial sums of an integer partition. St000679The pruning number of an ordered tree. St000684The global dimension of the LNakayama algebra associated to a Dyck path. St000686The finitistic dominant dimension of a Dyck path. St000758The length of the longest staircase fitting into an integer composition. St000760The length of the longest strictly decreasing subsequence of parts of an integer composition. St000764The number of strong records in an integer composition. St000783The side length of the largest staircase partition fitting into a partition. St000903The number of different parts of an integer composition. St000916The packing number of a graph. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. 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. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001339The irredundance number of a graph. St001432The order dimension of the partition. St001463The number of distinct columns in the nullspace of a graph. St001512The minimum rank of a graph. St001642The Prague dimension of a graph. St001644The dimension of a graph. St001732The number of peaks visible from the left. St001741The largest integer such that all patterns of this size are contained in the permutation. St001913The number of preimages of an integer partition in Bulgarian solitaire. St000271The chromatic index of a graph. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000548The number of different non-empty partial sums of an integer partition. St000876The number of factors in the Catalan decomposition of a binary word. St001093The detour number of a graph. St000061The number of nodes on the left branch of a binary tree. 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. 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 $eA$. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000472The sum of the ascent bottoms of a permutation. St000647The number of big descents of a permutation. St000654The first descent of a permutation. St000694The number of affine bounded permutations that project to a given permutation. St000781The number of proper colouring schemes of a Ferrers diagram. 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 $K[x]/(x^n)$. St001481The minimal height of a peak of a Dyck path. St001571The Cartan determinant of the integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. 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. St000353The number of inner valleys of a permutation. St000434The number of occurrences of the pattern 213 or of the pattern 312 in a permutation. St000435The number of occurrences of the pattern 213 or of the pattern 231 in a permutation. St000437The number of occurrences of the pattern 312 or of the pattern 321 in a permutation. St000461The rix statistic of a permutation. St000485The length of the longest cycle of a permutation. St000646The number of big ascents of a permutation. St000649The number of 3-excedences of a permutation. St000650The number of 3-rises of a permutation. St000711The number of big exceedences of a permutation. St000726The normalized sum of the leaf labels of the increasing binary tree associated to a permutation. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000804The number of occurrences of the vincular pattern |123 in a permutation. St000866The number of admissible inversions of a permutation in the sense of Shareshian-Wachs. St001005The number of indices for a permutation that are either left-to-right maxima or right-to-left minima but not both. St001082The number of boxed occurrences of 123 in a permutation. St001130The number of two successive successions in a permutation. St001174The Gorenstein dimension of the algebra $A/I$ when $I$ is the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001175The size of a partition minus the hook length of the base cell. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001346The number of parking functions that give the same permutation. St001363The Euler characteristic of a graph according to Knill. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001657The number of twos in an integer partition. St001691The number of kings in a graph. St000219The number of occurrences of the pattern 231 in a permutation. St001811The Castelnuovo-Mumford regularity of a permutation. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000528The height of a poset. St001343The dimension of the reduced incidence algebra of a poset. St001717The largest size of an interval in a poset. St000287The number of connected components of a graph. St001734The lettericity of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001116The game chromatic number of a graph. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St001095The number of non-isomorphic posets with precisely one further covering relation. St001545The second Elser number of a connected graph. St000454The largest eigenvalue of a graph if it is integral. St001625The Möbius invariant of a lattice. St000633The size of the automorphism group of a poset. St000850The number of 1/2-balanced pairs in a poset. 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. St000257The number of distinct parts of a partition that occur at least twice. St001877Number of indecomposable injective modules with projective dimension 2. 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. St000256The number of parts from which one can substract 2 and still get an integer partition. St000671The maximin edge-connectivity for choosing a subgraph. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001624The breadth of a lattice. St001315The dissociation number of a graph. St001110The 3-dynamic chromatic number of a graph. St000080The rank of the poset. St000284The Plancherel distribution on integer partitions. St000338The number of pixed points of a permutation. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000897The number of different multiplicities of parts of an integer partition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001128The exponens consonantiae of a partition. 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. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001349The number of different graphs obtained from the given graph by removing an edge. St001354The number of series nodes in the modular decomposition of a graph. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St000092The number of outer peaks of a permutation. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000299The number of nonisomorphic vertex-induced subtrees. St000567The sum of the products of all pairs of parts. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. 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. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. 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. 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. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001471The magnitude of a Dyck path. St001530The depth of a Dyck path. St001649The length of a longest trail in a graph. St001674The number of vertices of the largest induced star graph in the graph. St001890The maximum magnitude of the Möbius function of a poset. St000618The number of self-evacuating tableaux of given shape. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001948The number of augmented double ascents of a permutation. 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. St001520The number of strict 3-descents. St001557The number of inversions of the second entry of a permutation. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition.