St000568The hook number of a binary tree. St000884The number of isolated descents of a permutation. St001737The number of descents of type 2 in a permutation. St001928The number of non-overlapping descents in a permutation. St000470The number of runs in a permutation. St000619The number of cyclic descents of a permutation. St000703The number of deficiencies of a permutation. St000994The number of cycle peaks and the number of cycle valleys of a permutation. St001269The sum of the minimum of the number of exceedances and deficiencies in each cycle of a permutation. St001729The number of visible descents of a permutation. St001469The holeyness of a permutation. St000354The number of recoils of a permutation. St001665The number of pure excedances of a permutation. St000996The number of exclusive left-to-right maxima of a permutation. St000353The number of inner valleys of a permutation. St000632The jump number of the poset. St000662The staircase size of the code of a permutation. St000054The first entry of the permutation. St000035The number of left outer peaks of a permutation. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001216The number of indecomposable injective modules in the corresponding Nakayama algebra that have non-vanishing second Ext-group with the regular module. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001274The number of indecomposable injective modules with projective dimension equal to two. St001276The number of 2-regular indecomposable modules in the corresponding Nakayama algebra. St000781The number of proper colouring schemes of a Ferrers diagram. St001913The number of preimages of an integer partition in Bulgarian solitaire. St000660The number of rises of length at least 3 of a Dyck path. St000454The largest eigenvalue of a graph if it is integral. St000760The length of the longest strictly decreasing subsequence of parts of an integer composition. St001728The number of invisible descents of a permutation. St000779The tier of a permutation. St000245The number of ascents of a permutation. St000834The number of right outer peaks of a permutation. St000098The chromatic number of a graph. St000542The number of left-to-right-minima 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. St000659The number of rises of length at least 2 of a Dyck path. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001199The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. St000097The order of the largest clique of the graph. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000260The radius of a connected graph. St001085The number of occurrences of the vincular pattern |21-3 in a permutation. St001568The smallest positive integer that does not appear twice in the partition. St001685The number of distinct positions of the pattern letter 1 in occurrences of 132 in a permutation. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St000640The rank of the largest boolean interval in a poset. St000914The sum of the values of the Möbius function of a poset. St001682The number of distinct positions of the pattern letter 1 in occurrences of 123 in a permutation. St000897The number of different multiplicities of parts of an integer partition. St000618The number of self-evacuating tableaux of given shape. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000706The product of the factorials of the multiplicities of an integer partition. St000934The 2-degree of an integer partition. St000993The multiplicity of the largest part of an integer partition. St001128The exponens consonantiae of a partition. St001280The number of parts of an integer partition that are at least two. 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. St001564The value of the forgotten symmetric functions when all variables set to 1. 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. 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. St001780The order of promotion on the set of standard tableaux of given shape. 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. St001924The number of cells in an integer partition whose arm and leg length coincide. St001933The largest multiplicity of a part in an integer partition. St000093The cardinality of a maximal independent set of vertices of a graph. St001890The maximum magnitude of the Möbius function of a poset. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001181Number of indecomposable injective modules with grade at least 3 in the corresponding Nakayama algebra. St001086The number of occurrences of the consecutive pattern 132 in a permutation. St000711The number of big exceedences of a permutation. St001394The genus of a permutation. St000021The number of descents of a permutation. St000023The number of inner peaks of a permutation. St000099The number of valleys of a permutation, including the boundary. St000325The width of the tree associated to a permutation. St001471The magnitude of a Dyck path. St000155The number of exceedances (also excedences) of a permutation. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. St001744The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. St000092The number of outer peaks of a permutation. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001335The cardinality of a minimal cycle-isolating set of a graph. St001597The Frobenius rank of a skew partition. St000272The treewidth of a graph. St000535The rank-width of a graph. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001331The size of the minimal feedback vertex set. St001333The cardinality of a minimal edge-isolating set of a graph. St001358The largest degree of a regular subgraph of a graph. St001393The induced matching number of a graph. St001638The book thickness of a graph. St001644The dimension of a graph. St001743The discrepancy of a graph. St001792The arboricity of a graph. St001826The maximal number of leaves on a vertex of a graph. St001962The proper pathwidth of a graph. St000482The (zero)-forcing number of a graph. St000544The cop number of a graph. St001029The size of the core of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001352The number of internal nodes in the modular decomposition of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001883The mutual visibility number of a graph. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St001057The Grundy value of the game of creating an independent set in a graph. St001592The maximal number of simple paths between any two different vertices of a graph. St001427The number of descents of a signed permutation. St001498The normalised height of a Nakayama algebra with magnitude 1. St001732The number of peaks visible from the left. St000137The Grundy value of an integer partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St001122The multiplicity of the sign representation in the Kronecker square corresponding to 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. St001525The number of symmetric hooks on the diagonal of a partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001330The hat guessing number of a graph. St000455The second largest eigenvalue of a graph if it is integral. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001470The cyclic holeyness of a permutation. St000647The number of big descents of 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 $K[x]/(x^n)$. 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. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St000741The Colin de Verdière graph invariant. St001632The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset. St000527The width of the poset. St000298The order dimension or Dushnik-Miller dimension of a poset. St000256The number of parts from which one can substract 2 and still get an integer partition. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St000307The number of rowmotion orbits of a poset. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St000486The number of cycles of length at least 3 of a permutation. St000100The number of linear extensions of a poset. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000871The number of very big ascents of a permutation. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001877Number of indecomposable injective modules with projective dimension 2. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St000650The number of 3-rises of a permutation. St000665The number of rafts of a permutation. St000872The number of very big descents of a permutation. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000929The constant term of the character polynomial of an integer 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. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001810The number of fixed points of a permutation smaller than its largest moved point. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000306The bounce count of a Dyck path. St000451The length of the longest pattern of the form k 1 2. St000822The Hadwiger number of the graph. St001734The lettericity of a graph. St001323The independence gap of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001642The Prague dimension of a graph. St001820The size of the image of the pop stack sorting operator. St000254The nesting number of a set partition. St001621The number of atoms of a lattice. St001624The breadth of a lattice. St000845The maximal number of elements covered by an element in a poset. St000846The maximal number of elements covering an element of a poset. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000850The number of 1/2-balanced pairs in a poset. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000402Half the size of the symmetry class of 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. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. St001761The maximal multiplicity of a letter in a reduced word of a permutation. St001165Number of simple modules with even projective dimension in the corresponding Nakayama 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 $eA$. St000441The number of successions of a permutation. St000731The number of double exceedences of a permutation. St000966Number of peaks minus the global dimension 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. St001577The minimal number of edges to add or remove to make a graph a cograph. St001871The number of triconnected components of a graph. St000028The number of stack-sorts needed to sort a permutation. St001114The number of odd descents of a permutation. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001530The depth of a Dyck path. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001960The number of descents of a permutation minus one if its first entry is not one. St001520The number of strict 3-descents. St000386The number of factors DDU in a Dyck path. St001301The first Betti number of the order complex associated with the poset. St001396Number of triples of incomparable elements in a finite poset. St000862The number of parts of the shifted shape of a permutation. St000908The length of the shortest maximal antichain in a poset. St001399The distinguishing number of a poset. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001964The interval resolution global dimension of a poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St000181The number of connected components of the Hasse diagram for the poset. St000068The number of minimal elements in a poset. St000031The number of cycles in the cycle decomposition of a permutation. St001846The number of elements which do not have a complement in the lattice. St001720The minimal length of a chain of small intervals in a lattice. St001875The number of simple modules with projective dimension at most 1. St000768The number of peaks in an integer composition. St000807The sum of the heights of the valleys of the associated bargraph. St000848The balance constant multiplied with the number of linear extensions of a poset. St000849The number of 1/3-balanced pairs in a poset. St001397Number of pairs of incomparable elements in a finite poset. St000633The size of the automorphism group of a poset. St000910The number of maximal chains of minimal length in a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001268The size of the largest ordinal summand in the poset. St001779The order of promotion on the set of linear extensions of a poset. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St000058The order of a permutation. St000223The number of nestings in the permutation. St000371The number of mid points of decreasing subsequences of length 3 in a permutation. St000373The number of weak exceedences of a permutation that are also mid-points of a decreasing subsequence of length $3$. St001559The number of transpositions that are smaller or equal to a permutation in Bruhat order while not being inversions. St001487The number of inner corners of a skew partition. St001864The number of excedances of a signed permutation. St001866The nesting alignments of a signed permutation. St001868The number of alignments of type NE of a signed permutation. St001896The number of right descents of a signed permutations. St000630The length of the shortest palindromic decomposition of a binary word. St001435The number of missing boxes in the first row. St000920The logarithmic height of a Dyck path. St000891The number of distinct diagonal sums of a permutation matrix. St000624The normalized sum of the minimal distances to a greater element. St000007The number of saliances of the permutation. St000761The number of ascents in an integer composition. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000805The number of peaks of the associated bargraph. St001661Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation. St000252The number of nodes of degree 3 of a binary tree. St000296The length of the symmetric border of a binary word. St000297The number of leading ones in a binary word. St000534The number of 2-rises of a permutation. St000664The number of right ropes of a permutation. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001037The number of inner corners of the upper path of the parallelogram polyomino associated with the Dyck path. 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. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001423The number of distinct cubes in a binary word. St001438The number of missing boxes of a skew partition. St001513The number of nested exceedences of a permutation. St001549The number of restricted non-inversions between exceedances. St001556The number of inversions of the third entry of a permutation. St001823The Stasinski-Voll length of a signed permutation. St001905The number of preferred parking spots in a parking function less than the index of the car. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St001946The number of descents in a parking function. St001948The number of augmented double ascents of a permutation. St000314The number of left-to-right-maxima of a permutation. St000333The dez statistic, the number of descents of a permutation after replacing fixed points by zeros. St000710The number of big deficiencies of a permutation. St000864The number of circled entries of the shifted recording tableau of a permutation. 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. 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 $K[x]/(x^n)$. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001298The number of repeated entries in the Lehmer code of a permutation. St000758The length of the longest staircase fitting into an integer composition. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001582The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order. St001816Eigenvalues of the top-to-random operator acting on a simple module. St000253The crossing number of a set partition. St000764The number of strong records in an integer composition. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000237The number of small exceedances. St001465The number of adjacent transpositions in the cycle decomposition of a permutation. St000883The number of longest increasing subsequences of a permutation.