St001326The minimal number of occurrences of the interval-pattern in a linear ordering of the vertices of the graph. St001345The Hamming dimension of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001577The minimal number of edges to add or remove to make a graph a cograph. St001703The villainy of a graph. St001957The number of Hasse diagrams with a given underlying undirected graph. St000264The girth of a graph, which is not a tree. St001391The disjunction number of a graph. St001828The Euler characteristic of a graph. St000098The chromatic number of a graph. St000172The Grundy number of a graph. St000258The burning number of a graph. St000271The chromatic index of a graph. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000469The distinguishing number of a graph. St000636The hull number of a graph. St000697The number of 3-rim hooks removed from an integer partition to obtain its associated 3-core. St000762The sum of the positions of the weak records of an integer composition. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000820The number of compositions obtained by rotating the composition. St000822The Hadwiger number of the graph. St000918The 2-limited packing number of a graph. St001111The weak 2-dynamic chromatic number of a graph. St001112The 3-weak dynamic number of a graph. St001116The game chromatic number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001315The dissociation number of a graph. St001476The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,-1). St001478The number of nowhere zero 4-flows of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001591The number of graphs with the given composition of multiplicities of Laplacian eigenvalues. St001655The general position number of a graph. St001670The connected partition number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001883The mutual visibility number of a graph. St001931The weak major index of an integer composition regarded as a word. St000143The largest repeated part of a partition. St000150The floored half-sum of the multiplicities of a partition. St000171The degree of the graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000272The treewidth of a graph. St000310The minimal degree of a vertex of a graph. St000351The determinant of the adjacency matrix of a graph. St000387The matching number of a graph. St000454The largest eigenvalue of a graph if it is integral. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000535The rank-width of a graph. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St000766The number of inversions of an integer composition. St000769The major index of a composition regarded as a word. St000778The metric dimension of a graph. St000913The number of ways to refine the partition into singletons. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001270The bandwidth of a graph. St001271The competition number of a graph. St001277The degeneracy of a graph. St001281The normalized isoperimetric number of a graph. St001333The cardinality of a minimal edge-isolating set of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001358The largest degree of a regular subgraph of a graph. St001572The minimal number of edges to remove to make a graph bipartite. St001573The minimal number of edges to remove to make a graph triangle-free. St001592The maximal number of simple paths between any two different vertices of a graph. St001644The dimension of a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001742The difference of the maximal and the minimal degree in a graph. St001743The discrepancy of a graph. St001792The arboricity of a graph. St001910The height of the middle non-run of a Dyck path. St001949The rigidity index of a graph. St001962The proper pathwidth of a graph. St000363The number of minimal vertex covers of a graph. St000448The number of pairs of vertices of a graph with distance 2. St000722The number of different neighbourhoods in a graph. St001029The size of the core of a graph. St001108The 2-dynamic chromatic number of a graph. St001304The number of maximally independent sets of vertices of a graph. St001458The rank of the adjacency matrix of a graph. St001486The number of corners of the ribbon associated with an integer composition. St000384The maximal part of the shifted composition of an integer partition. St000459The hook length of the base cell of a partition. St000818The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions. St001389The number of partitions of the same length below the given integer partition. St001869The maximum cut size of a graph. St000088The row sums of the character table of the symmetric group. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000321The number of integer partitions of n that are dominated by an integer partition. St000345The number of refinements of a partition. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000812The sum of the entries in the column specified by the partition of the change of basis matrix from complete homogeneous symmetric functions to monomial symmetric functions. St000815The number of semistandard Young tableaux of partition weight of given shape. St000933The number of multipartitions of sizes given by an integer partition. St000935The number of ordered refinements of an integer partition. St000937The number of positive values of the symmetric group character corresponding to the partition. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001611The number of multiset partitions such that the multiplicities of elements are given by a partition. St001612The number of coloured multisets of cycles such that the multiplicities of colours are given by a partition. St000422The energy of a graph, if it is integral. St000915The Ore degree of a graph. St000104The number of facets in the order polytope of this poset. St000151The number of facets in the chain polytope of the poset. St001546The number of monomials in the Tutte polynomial of a graph. St001762The number of convex subsets of vertices in a graph. St000047The number of standard immaculate tableaux of a given shape. St000093The cardinality of a maximal independent set of vertices of a graph. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000295The length of the border of a binary word. St000322The skewness of a graph. St000323The minimal crossing number of a graph. St000331The number of upper interactions of a Dyck path. St000377The dinv defect of an integer partition. St000378The diagonal inversion number of an integer partition. St000390The number of runs of ones in a binary word. St000450The number of edges minus the number of vertices plus 2 of a graph. St000456The monochromatic index of a connected graph. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000644The number of graphs with given frequency partition. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000759The smallest missing part in an integer partition. St000763The sum of the positions of the strong records of an integer composition. St000765The number of weak records in an integer composition. St000767The number of runs in an integer composition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000808The number of up steps of the associated bargraph. 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. St000941The number of characters of the symmetric group whose value on the partition is even. St000952Gives the number of irreducible factors of the Coxeter polynomial of the Dyck path over the rational numbers. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001036The number of inner corners of the parallelogram polyomino associated with the Dyck path. St001057The Grundy value of the game of creating an independent set in a graph. St001102The number of words with multiplicities of the letters given by the composition, avoiding the consecutive pattern 132. St001117The game chromatic index of a graph. St001118The acyclic chromatic index of a graph. St001176The size of a partition minus its first part. 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. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001250The number of parts of a partition that are not congruent 0 modulo 3. St001282The number of graphs with the same chromatic polynomial. St001312Number of parabolic noncrossing partitions indexed by the composition. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001459The number of zero columns in the nullspace of a graph. St001463The number of distinct columns in the nullspace of a graph. St001487The number of inner corners of a skew partition. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001601The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on trees. St001694The number of maximal dissociation sets in a graph. St001716The 1-improper chromatic number of a graph. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001739The number of graphs with the same edge polytope as the given graph. 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. St001939The number of parts that are equal to their multiplicity in the integer partition. St001955The number of natural descents for set-valued two row standard Young tableaux. St000008The major index of the composition. St000089The absolute variation of a composition. St000095The number of triangles of a graph. St000097The order of the largest clique of the graph. St000142The number of even parts of a partition. St000149The number of cells of the partition whose leg is zero and arm is odd. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000185The weighted size of a partition. St000268The number of strongly connected orientations of a graph. St000291The number of descents of a binary word. St000292The number of ascents of a binary word. St000313The number of degree 2 vertices of a graph. St000340The number of non-final maximal constant sub-paths of length greater than one. St000346The number of coarsenings of a partition. St000376The bounce deficit of a Dyck path. St000388The number of orbits of vertices of a graph under automorphisms. St000403The Szeged index minus the Wiener index of a graph. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000519The largest length of a factor maximising the subword complexity. St000531The leading coefficient of the rook polynomial of an integer partition. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000658The number of rises of length 2 of a Dyck path. St000681The Grundy value of Chomp on Ferrers diagrams. St000691The number of changes of a binary word. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000770The major index of an integer partition when read from bottom to top. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000921The number of internal inversions of a binary word. St000922The minimal number such that all substrings of this length are unique. St000939The number of characters of the symmetric group whose value on the partition is positive. St000940The number of characters of the symmetric group whose value on the partition is zero. St000992The alternating sum of the parts of an integer partition. St000995The largest even part of an integer partition. St001033The normalized area of the parallelogram polyomino associated with the Dyck path. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001139The number of occurrences of hills of size 2 in a Dyck path. St001214The aft of an integer partition. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001252Half the sum of the even parts of a partition. St001263The index of the maximal parabolic seaweed algebra associated with the composition. St001280The number of parts of an integer partition that are at least two. St001299The product of all non-zero projective dimensions of simple modules of the corresponding Nakayama algebra. St001311The cyclomatic number of a graph. St001317The minimal number of occurrences of the forest-pattern in a linear ordering of the vertices of the graph. St001319The minimal number of occurrences of the star-pattern in a linear ordering of the vertices of the graph. St001323The independence gap of a graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001331The size of the minimal feedback vertex set. St001352The number of internal nodes in the modular decomposition of a graph. St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001414Half the length of the longest odd length palindromic prefix 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. St001435The number of missing boxes in the first row. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001500The global dimension of magnitude 1 Nakayama algebras. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001647The number of edges that can be added without increasing the clique number. St001648The number of edges that can be added without increasing the chromatic number. St001657The number of twos in an integer partition. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001689The number of celebrities in a graph. St001692The number of vertices with higher degree than the average degree in a graph. St001746The coalition number of a graph. St001774The degree of the minimal polynomial of the smallest eigenvalue of a graph. St001775The degree of the minimal polynomial of the largest eigenvalue of a graph. St001777The number of weak descents in an integer composition. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St001814The number of partitions interlacing the given partition. 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. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St001961The sum of the greatest common divisors of all pairs of parts. St001963The tree-depth of a graph. St000003The number of standard Young tableaux of the partition. St000081The number of edges of a graph. St000347The inversion sum of a binary word. St000348The non-inversion sum of a binary word. St000477The weight of a partition according to Alladi. St000548The number of different non-empty partial sums of an integer partition. St000631The number of distinct palindromic decompositions of a binary word. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000878The number of ones minus the number of zeros of a binary word. St000928The sum of the coefficients of the character polynomial of an integer 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. St001182Number of indecomposable injective modules with codominant dimension at least two in the corresponding Nakayama algebra. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001308The number of induced paths on three vertices in a graph. St001313The number of Dyck paths above the lattice path given by a binary word. St001341The number of edges in the center of a graph. St001350Half of the Albertson index of a graph. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001473The absolute value of the sum of all entries of the Coxeter matrix of the corresponding LNakayama algebra. St001488The number of corners of a skew partition. St001527The cyclic permutation representation number of an integer partition. St001725The harmonious chromatic number of a graph. St001872The number of indecomposable injective modules with even projective dimension in the corresponding Nakayama algebra. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St000311The number of vertices of odd degree in a graph. St000668The least common multiple of the parts of the partition. St000867The sum of the hook lengths in the first row of an integer partition. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001110The 3-dynamic chromatic number of a graph. St001386The number of prime labellings of a graph. St001541The Gini index of an integer partition. St000145The Dyson rank of a partition. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St001019Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St000567The sum of the products of all pairs of parts. St000979Half of MacMahon's equal index of a Dyck path. St000997The even-odd crank of an integer partition. St001213The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module. St001501The dominant dimension of magnitude 1 Nakayama algebras. St000108The number of partitions contained in the given partition. St000438The position of the last up step in a Dyck path. St001065Number of indecomposable reflexive modules in the corresponding Nakayama algebra. St001643The Frobenius dimension of the Nakayama algebra corresponding to the Dyck path. St001721The degree of a binary word. St000027The major index of a Dyck path. St000301The number of facets of the stable set polytope of a graph. St000817The sum of the entries in the column specified by the composition of the change of basis matrix from dual immaculate quasisymmetric functions to monomial quasisymmetric functions. St000981The length of the longest zigzag subpath. St001259The vector space dimension of the double dual of D(A) in the corresponding Nakayama algebra. St001669The number of single rises in a Dyck path. St000300The number of independent sets of vertices of a graph. St000294The number of distinct factors of a binary word. St000518The number of distinct subsequences in a binary word. St001706The number of closed sets in a graph. St000455The second largest eigenvalue of a graph if it is integral. St000741The Colin de Verdière graph invariant. St000718The largest Laplacian eigenvalue of a graph if it is integral. St001103The number of words with multiplicities of the letters given by the partition, avoiding the consecutive pattern 123. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001442The number of standard Young tableaux whose major index is divisible by the size of a given integer partition. 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. St001711The number of permutations such that conjugation with a permutation of given cycle type yields the squared permutation. 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. St001609The number of coloured trees such that the multiplicities of colours are given by a partition. St001710The number of permutations such that conjugation with a permutation of given cycle type yields the inverse permutation. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001330The hat guessing number of a graph. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001628The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs. St001607The number of coloured graphs such that the multiplicities of colours are given by a partition. St000046The largest eigenvalue of the random to random operator acting on the simple module corresponding to the given partition. St001763The Hurwitz number of an integer partition. St000479The Ramsey number of a graph. St001610The number of coloured endofunctions such that the multiplicities of colours are given by a partition. St001834The number of non-isomorphic minors of a graph. St001545The second Elser number of a connected graph. St001529The number of monomials in the expansion of the nabla operator applied to the power-sum symmetric function indexed by the partition. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St001195The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$. 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. St001616The number of neutral elements in a lattice. St001618The cardinality of the Frattini sublattice of a lattice. St001624The breadth of a lattice. St001625The Möbius invariant of a lattice. St001679The number of subsets of a lattice whose meet is the bottom element. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001720The minimal length of a chain of small intervals in a lattice. St001754The number of tolerances of a finite lattice. St001820The size of the image of the pop stack sorting operator. St001833The number of linear intervals in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St000379The number of Hamiltonian cycles in a graph. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000699The toughness times the least common multiple of 1,. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. 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 $eA$. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001613The binary logarithm of the size of the center of a lattice. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St001619The number of non-isomorphic sublattices of a lattice. St001620The number of sublattices of a lattice. St001621The number of atoms of a lattice. St001622The number of join-irreducible elements of a lattice. St001623The number of doubly irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St001666The number of non-isomorphic subposets of a lattice which are lattices. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001845The number of join irreducibles minus the rank of a lattice. St001846The number of elements which do not have a complement in the lattice. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001570The minimal number of edges to add to make a graph Hamiltonian. St001645The pebbling number of a connected graph. St001812The biclique partition number of a graph. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St000950Number of tilting modules of the corresponding LNakayama algebra, where a tilting module is a generalised tilting module of projective dimension 1. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St001243The sum of coefficients in the Schur basis of certain LLT polynomials associated with a Dyck path. St001242The toal dimension of certain Sn modules determined by LLT polynomials associated with a Dyck path. St001256Number of simple reflexive modules that are 2-stable reflexive. 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. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001113Number of indecomposable projective non-injective modules with reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001873For a Nakayama algebra corresponding to a Dyck path, we define the matrix C with entries the Hom-spaces between $e_i J$ and $e_j J$ (the radical of the indecomposable projective modules). St001480The number of simple summands of the module J^2/J^3. 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 $c_{n−1}$. St000618The number of self-evacuating tableaux of given shape. St000667The greatest common divisor of the parts of the partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000781The number of proper colouring schemes of a Ferrers diagram. St001432The order dimension of the partition. St001571The Cartan determinant of the integer partition. St001780The order of promotion on the set of standard tableaux of given shape. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St000225Difference between largest and smallest parts in a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. 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. St000944The 3-degree of an integer partition. St001175The size of a partition minus the hook length of the base cell. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001248Sum of the even parts of a partition. St001279The sum of the parts of an integer partition that are at least two. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St001587Half of the largest even part of an integer partition. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000284The Plancherel distribution on integer partitions. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000901The cube of the number of standard Young tableaux with shape given by the partition. St000929The constant term of the character polynomial of an integer partition. St001128The exponens consonantiae of a partition. St000464The Schultz index of a connected graph. St000478Another weight of a partition according to Alladi. St000934The 2-degree of an integer partition. 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. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001568The smallest positive integer that does not appear twice in the partition. St000475The number of parts equal to 1 in a partition. St001122The multiplicity of the sign representation in the Kronecker square corresponding to a partition. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St000474Dyson's crank of a partition. St000784The maximum of the length and the largest part of the integer partition. St001651The Frankl number of a lattice. St000068The number of minimal elements 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. St001875The number of simple modules with projective dimension at most 1. St000508Eigenvalues of the random-to-random operator acting on a simple module. St000953The largest degree of an irreducible factor of the Coxeter polynomial of the Dyck path over the rational numbers. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001722The number of minimal chains with small intervals between a binary word and the top element. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001438The number of missing boxes of a skew partition. St001023Number of simple modules with projective dimension at most 3 in the Nakayama algebra corresponding to the Dyck path. St000181The number of connected components of the Hasse diagram for the poset. St000908The length of the shortest maximal antichain in a poset. St001301The first Betti number of the order complex associated with the poset. St001060The distinguishing index of a graph. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St001890The maximum magnitude of the Möbius function of a poset. St000273The domination number of a graph. St000327The number of cover relations in a poset. 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. St000544The cop number of a graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000917The open packing number of a graph. St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St001637The number of (upper) dissectors of a poset. St001654The monophonic hull number of a graph. St001668The number of points of the poset minus the width of the poset. St001829The common independence number of a graph. St000553The number of blocks of a graph. St000671The maximin edge-connectivity for choosing a subgraph. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000775The multiplicity of the largest eigenvalue in a graph. St001353The number of prime nodes in the modular decomposition of a graph. St001496The number of graphs with the same Laplacian spectrum as the given graph. St001740The number of graphs with the same symmetric edge polytope as the given graph. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000302The determinant of the distance matrix of a connected graph. St000312The number of leaves in a graph. St000370The genus of a graph. St000449The number of pairs of vertices of a graph with distance 4. St000552The number of cut vertices of a graph. St001307The number of induced stars on four vertices in a graph. St001309The number of four-cliques in a graph. St001310The number of induced diamond graphs in a graph. St001334The minimal number of occurrences of the 3-colorable pattern in a linear ordering of the vertices of the graph. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001354The number of series nodes in the modular decomposition of a graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St001479The number of bridges of a graph. St001691The number of kings in a graph. St001826The maximal number of leaves on a vertex of a graph. St000467The hyper-Wiener index of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000635The number of strictly order preserving maps of a poset into itself. St000023The number of inner peaks of a permutation. St000056The decomposition (or block) number of a permutation. St000162The number of nontrivial cycles in the cycle decomposition of a permutation. St000362The size of a minimal vertex cover of a graph. St000486The number of cycles of length at least 3 of a permutation. St000694The number of affine bounded permutations that project to a given permutation. St000732The number of double deficiencies of a permutation. St000779The tier of a permutation. St000788The number of nesting-similar perfect matchings of a perfect matching. St000882The number of connected components of short braid edges in the graph of braid moves of a permutation. St000914The sum of the values of the Möbius function of a poset. St000930The k-Gorenstein degree of the corresponding Nakayama algebra with linear quiver. St001006Number of simple modules with projective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001081The number of minimal length factorizations of a permutation into star transpositions. 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 $K[x]/(x^n)$. St001294The maximal torsionfree index of a simple non-projective module in the corresponding Nakayama algebra. St001327The minimal number of occurrences of the split-pattern in a linear ordering of the vertices of the graph. St001461The number of topologically connected components of the chord diagram of a permutation. St001493The number of simple modules with maximal even projective dimension in the corresponding Nakayama algebra. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001520The number of strict 3-descents. St001556The number of inversions of the third entry of a permutation. St001590The crossing number of a perfect matching. St001593This is the number of standard Young tableaux of the given shifted shape. St001661Half the permanent of the Identity matrix plus the permutation matrix associated to the permutation. St001830The chord expansion number of a perfect matching. St001832The number of non-crossing perfect matchings in the chord expansion of a perfect matching. St001859The number of factors of the Stanley symmetric function associated with a permutation. St001913The number of preimages of an integer partition in Bulgarian solitaire. St001933The largest multiplicity of a part in an integer partition. St001936The number of transitive factorisations of a permutation of given cycle type into star transpositions. St001938The number of transitive monotone factorizations of genus zero of a permutation of given cycle type. St000099The number of valleys of a permutation, including the boundary. St000193The row of the unique '1' in the first column of the alternating sign matrix. St000221The number of strong fixed points of a permutation. St000243The number of cyclic valleys and cyclic peaks of a permutation. St000279The size of the preimage of the map 'cycle-as-one-line notation' from Permutations to Permutations. St000368The Altshuler-Steinberg determinant of a graph. St000375The number of non weak exceedences of a permutation that are mid-points of a decreasing subsequence of length $3$. St000482The (zero)-forcing number of a graph. St000488The number of cycles of a permutation of length at most 2. St000489The number of cycles of a permutation of length at most 3. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000623The number of occurrences of the pattern 52341 in a permutation. St000642The size of the smallest orbit of antichains under Panyushev complementation. St000643The size of the largest orbit of antichains under Panyushev complementation. St000666The number of right tethers of a permutation. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000787The number of flips required to make a perfect matching noncrossing. St000879The number of long braid edges in the graph of braid moves of a permutation. St000926The clique-coclique number of a graph. St000948The chromatic discriminant of a graph. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001041The depth of the label 1 in the decreasing labelled binary unordered tree associated with the perfect matching. St001043The depth of the leaf closest to the root in the binary unordered tree associated with the perfect matching. St001044The number of pairs whose larger element is at most one more than half the size of the perfect matching. St001059Number of occurrences of the patterns 41352,42351,51342,52341 in a permutation. St001095The number of non-isomorphic posets with precisely one further covering relation. St001131The number of trivial trees on the path to label one in the decreasing labelled binary unordered tree associated with the perfect matching. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001177Twice the mean value of the major index among all standard Young tableaux of a partition. St001184Number of indecomposable injective modules with grade at least 1 in the corresponding Nakayama algebra. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. 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. 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. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra. St001286The annihilation number of a graph. St001292The injective dimension of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. St001316The domatic number of a graph. St001359The number of permutations in the equivalence class of a permutation obtained by taking inverses of cycles. St001381The fertility of a permutation. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001444The rank of the skew-symmetric form which is non-zero on crossing arcs of a perfect matching. St001466The number of transpositions swapping cyclically adjacent numbers in a permutation. St001469The holeyness of a permutation. St001475The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,0). St001477The number of nowhere zero 5-flows of a graph. St001481The minimal height of a peak of a Dyck path. St001549The number of restricted non-inversions between exceedances. 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. St001557The number of inversions of the second entry of a permutation. St001569The maximal modular displacement of a permutation. St001597The Frobenius rank of a skew partition. St001656The monophonic position number of a graph. St001663The number of occurrences of the Hertzsprung pattern 132 in a permutation. St001714The number of subpartitions of an integer partition that do not dominate the conjugate subpartition. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001776The degree of the minimal polynomial of the largest Laplacian eigenvalue of a graph. St001810The number of fixed points of a permutation smaller than its largest moved point. St001811The Castelnuovo-Mumford regularity of a permutation. St001831The multiplicity of the non-nesting perfect matching in the chord expansion of a perfect matching. St001837The number of occurrences of a 312 pattern in the restricted growth word of a perfect matching. St001850The number of Hecke atoms of a permutation. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St000037The sign of a permutation. St000096The number of spanning trees of a graph. St000137The Grundy value of an integer partition. St000267The number of maximal spanning forests contained in a graph. St000286The number of connected components of the complement of a graph. St000287The number of connected components of a graph. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. St000309The number of vertices with even degree. St000344The number of strongly connected outdegree sequences of a graph. St000460The hook length of the last cell along the main diagonal of an integer partition. St000524The number of posets with the same order polynomial. St000525The number of posets with the same zeta polynomial. St000526The number of posets with combinatorially isomorphic order polytopes. St000637The length of the longest cycle in a graph. St000639The number of relations in a poset. St000641The number of non-empty boolean intervals in a poset. St000680The Grundy value for Hackendot on posets. St000706The product of the factorials of the multiplicities of an integer partition. St000717The number of ordinal summands of a poset. St000785The number of distinct colouring schemes of a graph. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000906The length of the shortest maximal chain in a poset. St000910The number of maximal chains of minimal length in a poset. St000916The packing number of a graph. St000993The multiplicity of the largest part of an integer partition. St001056The Grundy value for the game of deleting vertices of a graph until it has no edges. St001071The beta invariant of the graph. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001249Sum of the odd parts of a partition. St001272The number of graphs with the same degree sequence. St001302The number of minimally dominating sets of vertices of a graph. St001306The number of induced paths on four vertices in a graph. St001324The minimal number of occurrences of the chordal-pattern in a linear ordering of the vertices of the graph. St001325The minimal number of occurrences of the comparability-pattern in a linear ordering of the vertices of the graph. St001342The number of vertices in the center of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001356The number of vertices in prime modules of a graph. St001360The number of covering relations in Young's lattice below a partition. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001383The BG-rank of an integer partition. St001393The induced matching number of a graph. St001518The number of graphs with the same ordinary spectrum as the given graph. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001638The book thickness of a graph. St001667The maximal size of a pair of weak twins for a permutation. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001736The total number of cycles in a graph. St001783The number of odd automorphisms of a graph. St001793The difference between the clique number and the chromatic number of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001796The absolute value of the quotient of the Tutte polynomial of the graph at (1,1) and (-1,-1). St001797The number of overfull subgraphs of a graph. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St000266The number of spanning subgraphs of a graph with the same connected components. St000274The number of perfect matchings of a graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. 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. St000315The number of isolated vertices of a graph. St000447The number of pairs of vertices of a graph with distance 3. St000640The rank of the largest boolean interval in a poset. St000840The number of closers smaller than the largest opener in a perfect matching. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St001069The coefficient of the monomial xy of the Tutte polynomial of the graph. 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. St001247The number of parts of a partition that are not congruent 2 modulo 3. 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. St001305The number of induced cycles on four vertices in a graph. St001329The minimal number of occurrences of the outerplanar pattern in a linear ordering of the vertices of the graph. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001351The Albertson index of a graph. St001363The Euler characteristic of a graph according to Knill. St001395The number of strictly unfriendly partitions of a graph. St001521Half the total irregularity of a graph. St001522The total irregularity of a graph. St001525The number of symmetric hooks on the diagonal of a partition. St001561The value of the elementary symmetric function evaluated at 1. St001574The minimal number of edges to add or remove to make a graph regular. St001576The minimal number of edges to add or remove to make a graph vertex transitive. St001578The minimal number of edges to add or remove to make a graph a line graph. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001646The number of edges that can be added without increasing the maximal degree of a graph. St001690The length of a longest path in a graph such that after removing the paths edges, every vertex of the path has distance two from some other vertex of the path. St001708The number of pairs of vertices of different degree in a graph. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001795The binary logarithm of the evaluation of the Tutte polynomial of the graph at (x,y) equal to (-1,-1). St001871The number of triconnected components of a graph. St000087The number of induced subgraphs. 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. St000209Maximum difference of elements in cycles. St000210Minimum over maximum difference of elements in cycles. St000216The absolute length of a permutation. St000656The number of cuts of a poset. St000727The largest label of a leaf in the binary search tree associated with the permutation. St000740The last entry of a permutation. St000809The reduced reflection length of the permutation. St000924The number of topologically connected components of a perfect matching. St001077The prefix exchange distance of a permutation. St001958The degree of the polynomial interpolating the values of a permutation. St000086The number of subgraphs. St000485The length of the longest cycle of a permutation. St000487The length of the shortest cycle of a permutation. St000501The size of the first part in the decomposition of a permutation. St000673The number of non-fixed points of a permutation. St000844The size of the largest block in the direct sum decomposition of a permutation. St000927The alternating sum of the coefficients of the character polynomial of an integer partition. 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. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001468The smallest fixpoint of a permutation. St000244The cardinality of the automorphism group of a graph. St000350The sum of the vertex degrees of a graph. St000364The exponent of the automorphism group of a graph. St000401The size of the symmetry class of a permutation. St000509The diagonal index (content) of a partition. St000849The number of 1/3-balanced pairs in a poset. St000850The number of 1/2-balanced pairs in a poset. St001374The Padmakar-Ivan index of a graph. St001799The number of proper separations of a graph. St001802The number of endomorphisms of a graph. St001827The number of two-component spanning forests of a graph. St000468The Hosoya index of a graph. St000841The largest opener of a perfect matching. St000134The size of the orbit of an alternating sign matrix under gyration. St000349The number of different adjacency matrices of a graph. St000265The Wiener index of a graph. St001764The number of non-convex subsets of vertices in a graph. St000263The Szeged index of a graph. St000361The second Zagreb index of a graph. St000465The first Zagreb index of a graph. St001765The number of connected components of the friends and strangers graph. St001303The number of dominating sets of vertices of a graph. St001441The number of non-empty connected induced subgraphs of a graph. St001917The order of toric promotion on the set of labellings of a graph. St001262The dimension of the maximal parabolic seaweed algebra corresponding to the partition. St000972The composition number of a graph. St001474The evaluation of the Tutte polynomial of the graph at (x,y) equal to (2,-1). St000269The number of acyclic orientations of a graph. St001109The number of proper colourings of a graph with as few colours as possible. St001757The number of orbits of toric promotion on a graph. St000270The number of forests contained in a graph. St000343The number of spanning subgraphs of a graph. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St000571The F-index (or forgotten topological index) of a graph. St001758The number of orbits of promotion on a graph. St001602The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions. St001731The factorization defect of a permutation. St001943The sum of the squares of the hook lengths of an integer partition. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St000848The balance constant multiplied with the number of linear extensions of a poset. St001362The normalized Knill dimension of a graph. St000100The number of linear extensions of a poset. St000633The size of the automorphism group of a poset. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001378The product of the cohook lengths of the integer partition. St000690The size of the conjugacy class of a permutation. St001560The product of the cardinalities of the lower order ideal and upper order ideal generated by a permutation in weak order. St001072The evaluation of the Tutte polynomial of the graph at x and y equal to 3. St000716The dimension of the irreducible representation of Sp(6) labelled by an integer partition. St001528The number of permutations such that the product with the permutation has the same number of fixed points. St000634The number of endomorphisms of a poset. 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. St001290The first natural number n such that the tensor product of n copies of D(A) is zero for the corresponding Nakayama algebra A. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module 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 $eA$. St001013Number of indecomposable injective modules with codominant dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. 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. 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 $g$. 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. St001140Number of indecomposable modules with projective and injective dimension at least two in the corresponding Nakayama algebra. St001221The number of simple modules in the corresponding LNakayama algebra that have 2 dimensional second Extension group with the regular module. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St000079The number of alternating sign matrices for a given Dyck path. St000120The number of left tunnels of a Dyck path. St000964Gives the dimension of Ext^g(D(A),A) of the corresponding LNakayama algebra, when g denotes the global dimension of that algebra. St000965The sum of the dimension of Ext^i(D(A),A) for i=1,. St001010Number of indecomposable injective modules with projective dimension g-1 when g is the global dimension of the Nakayama algebra corresponding to the Dyck path. St001180Number of indecomposable injective modules with projective dimension at most 1. St001201The grade of the simple module $S_0$ in the special CNakayama algebra corresponding to the Dyck path. 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. St001229The vector space dimension of the first extension group between the Jacobson radical J and J^2. St001233The number of indecomposable 2-dimensional modules with projective dimension one. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001530The depth of a Dyck path. St000005The bounce statistic of a Dyck path. St000015The number of peaks of a Dyck path. St000117The number of centered tunnels of a Dyck path. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000335The difference of lower and upper interactions. St000967The value p(1) for the Coxeterpolynomial p of the corresponding LNakayama algebra. St000999Number of indecomposable projective module with injective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001017Number of indecomposable injective modules with projective dimension equal to the codominant dimension in the Nakayama algebra corresponding to the Dyck path. St001024Maximum of dominant dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001164Number of indecomposable injective modules whose socle has projective dimension at most g-1 (g the global dimension) minus the number of indecomposable projective-injective modules. St001181Number of indecomposable injective modules with grade at least 3 in the corresponding Nakayama algebra. St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. 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. St001215Let X be the direct sum of all simple modules of 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. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module. St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001241The number of non-zero radicals of the indecomposable projective modules that have injective dimension and projective dimension at most one. St001266The largest vector space dimension of an indecomposable non-projective module that is reflexive in the corresponding Nakayama algebra. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001274The number of indecomposable injective modules with projective dimension equal to two. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001296The maximal torsionfree index of an indecomposable non-projective module in the corresponding Nakayama algebra. St001503The largest distance of a vertex to a vertex in a cycle in the resolution quiver of the corresponding Nakayama algebra. St000006The dinv of a Dyck path. St000144The pyramid weight of the Dyck path. St000443The number of long tunnels of a Dyck path. St001008Number of indecomposable injective modules with projective dimension 1 in the Nakayama algebra corresponding to the Dyck path. St001014Number of indecomposable injective modules with codominant dimension equal to the dominant dimension of the Nakayama algebra corresponding to the Dyck path. St001015Number of indecomposable injective modules with codominant dimension equal to one in the Nakayama algebra corresponding to the Dyck path. St001016Number of indecomposable injective modules with codominant dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. 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. St001159Number of simple modules with dominant dimension equal to the global dimension in the corresponding Nakayama algebra. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001187The number of simple modules with grade at least one 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 $eA$. 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. St001224Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001238The number of simple modules S such that the Auslander-Reiten translate of S is isomorphic to the Nakayama functor applied to the second syzygy of S. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. 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. St001297The number of indecomposable non-injective projective modules minus the number of indecomposable non-injective projective modules that have reflexive Auslander-Reiten sequences in the corresponding Nakayama algebra. St001594The number of indecomposable projective modules in the Nakayama algebra corresponding to the Dyck path such that the UC-condition is satisfied. St000954Number of times the corresponding LNakayama algebra has $Ext^i(D(A),A)=0$ for $i>0$. St001018Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001021Sum of the differences between projective and codominant dimension of the non-projective indecomposable injective modules in the Nakayama algebra corresponding to the Dyck path. St001163The number of simple modules with dominant dimension at least three in the corresponding Nakayama algebra. St001230The number of simple modules with injective dimension equal to the dominant dimension equal to one and the dual property. St001231The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. St001234The number of indecomposable three dimensional modules with projective dimension one. St001218Smallest index k greater than or equal to one such that the Coxeter matrix C of the corresponding Nakayama algebra has C^k=1. St000527The width of the poset. St000071The number of maximal chains in a poset.