St001335The cardinality of a minimal cycle-isolating set of a graph. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001820The size of the image of the pop stack sorting operator. St000281The size of the preimage of the map 'to poset' from Binary trees to Posets. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000323The minimal crossing number of a graph. St000370The genus of a graph. St000379The number of Hamiltonian cycles in a graph. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St001301The first Betti number of the order complex associated with the poset. 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. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001510The number of self-evacuating linear extensions of a finite poset. St001651The Frankl number of a lattice. St001793The difference between the clique number and the chromatic number of a graph. St001797The number of overfull subgraphs of a 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. St001957The number of Hasse diagrams with a given underlying undirected graph. St001112The 3-weak dynamic number of a graph. St001116The game chromatic number of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001962The proper pathwidth of a graph. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000260The radius of a connected graph. St000272The treewidth of a graph. St000273The domination number of a graph. St000536The pathwidth of a graph. St000544The cop number of a graph. St000636The hull number of a graph. St001029The size of the core of a graph. St001109The number of proper colourings of a graph with as few colours as possible. St001111The weak 2-dynamic chromatic number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001277The degeneracy of a graph. St001322The size of a minimal independent dominating set in a graph. St001339The irredundance number of a graph. St001358The largest degree of a regular subgraph of a graph. St001654The monophonic hull number of a graph. St001689The number of celebrities in a graph. St001716The 1-improper chromatic number of a graph. St001792The arboricity of a graph. St000256The number of parts from which one can substract 2 and still get an integer partition. St000535The rank-width of a graph. St000667The greatest common divisor of the parts of the partition. St000671The maximin edge-connectivity for choosing a subgraph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000785The number of distinct colouring schemes of a graph. St000993The multiplicity of the largest part of an integer partition. St001272The number of graphs with the same degree sequence. St001316The domatic number of a graph. St001331The size of the minimal feedback vertex set. St001333The cardinality of a minimal edge-isolating set of a graph. St001354The number of series nodes in the modular decomposition of a graph. St001393The induced matching number of a graph. St001395The number of strictly unfriendly partitions of a graph. St001496The number of graphs with the same Laplacian spectrum as the given graph. St001621The number of atoms of a lattice. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St000351The determinant of the adjacency matrix of a graph. St000368The Altshuler-Steinberg determinant of a graph. St000449The number of pairs of vertices of a graph with distance 4. St000478Another weight of a partition according to Alladi. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000699The toughness times the least common multiple of 1,. St000929The constant term of the character polynomial of an integer partition. St000948The chromatic discriminant of a graph. St001119The length of a shortest maximal path in a graph. St001271The competition number of a graph. St001281The normalized isoperimetric number of a graph. St001305The number of induced cycles on four vertices in a graph. St001307The number of induced stars on four vertices in a graph. St001323The independence gap of 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. St001326The minimal number of occurrences of the interval-pattern in a linear ordering of the vertices of the graph. St001327The minimal number of occurrences of the split-pattern in a linear ordering of the vertices of the graph. St001328The minimal number of occurrences of the bipartite-pattern in a linear ordering of the vertices of the graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001367The smallest number which does not occur as degree of a vertex in a graph. St001618The cardinality of the Frattini sublattice of a lattice. St001623The number of doubly irreducible elements of a lattice. St001625The Möbius invariant of a lattice. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. 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). St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St001877Number of indecomposable injective modules with projective dimension 2. St001890The maximum magnitude of the Möbius function of a poset. St000322The skewness of a graph. St001626The number of maximal proper sublattices of a lattice. St000907The number of maximal antichains of minimal length in a poset. St001638The book thickness of a graph. St000181The number of connected components of the Hasse diagram for the poset. St000908The length of the shortest maximal antichain in a poset. St000914The sum of the values of the Möbius function of a poset. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001942The number of loops of the quiver corresponding to the reduced incidence algebra of a poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St001396Number of triples of incomparable elements in a finite poset. St001964The interval resolution global dimension of a poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. 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. St001568The smallest positive integer that does not appear twice in the partition. St001518The number of graphs with the same ordinary spectrum as the given graph. St000095The number of triangles of a graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St001573The minimal number of edges to remove to make a graph triangle-free. 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. St001871The number of triconnected components of a graph. St000282The size of the preimage of the map 'to poset' from Ordered trees to Posets. St001644The dimension of a graph. St000455The second largest eigenvalue of a graph if it is integral. St000266The number of spanning subgraphs of a graph with the same connected components. St000267The number of maximal spanning forests contained in a graph. St001475The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,0). St001476The evaluation of the Tutte polynomial of the graph at (x,y) equal to (1,-1). St001546The number of monomials in the Tutte polynomial of a graph. St000403The Szeged index minus the Wiener index of a graph. St000637The length of the longest cycle in a graph. St001069The coefficient of the monomial xy of the Tutte polynomial of the graph. 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. St001320The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. St001329The minimal number of occurrences of the outerplanar pattern in a linear ordering of the vertices of the graph. St001736The total number of cycles in a graph. St001795The binary logarithm of the evaluation of the Tutte polynomial of the graph at (x,y) equal to (-1,-1). St001875The number of simple modules with projective dimension at most 1. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St000822The Hadwiger number of the graph. St000299The number of nonisomorphic vertex-induced subtrees. St001642The Prague dimension of a graph. St001734The lettericity of a graph. St000286The number of connected components of the complement of a graph. St000287The number of connected components of a graph. St001391The disjunction number of a graph. St000096The number of spanning trees of a graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000274The number of perfect matchings of a graph. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. St000310The minimal degree of a vertex of a graph. St000315The number of isolated vertices of a graph. St000447The number of pairs of vertices of a graph with distance 3. St001345The Hamming dimension of a graph. St001572The minimal number of edges to remove to make a graph bipartite. St001575The minimal number of edges to add or remove to make a graph edge transitive. St001577The minimal number of edges to add or remove to make a graph a cograph. St001578The minimal number of edges to add or remove to make a graph a line graph. St001783The number of odd automorphisms of a graph. St001827The number of two-component spanning forests of a graph. St000741The Colin de Verdière graph invariant. St001668The number of points of the poset minus the width of the poset. St000327The number of cover relations in a poset. St001637The number of (upper) dissectors of a poset. St000635The number of strictly order preserving maps of a poset into itself. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001703The villainy of a graph. 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. St000257The number of distinct parts of a partition that occur at least twice. St000318The number of addable cells of the Ferrers diagram of an integer partition. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001203We associate to a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n-1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a Dyck path as follows: St001267The length of the Lyndon factorization of the binary word. St001471The magnitude of a Dyck path. St000159The number of distinct parts of the integer partition. St000183The side length of the Durfee square of an integer partition. St000259The diameter of a connected graph. St000295The length of the border of a binary word. St000306The bounce count of a Dyck path. St000439The position of the first down step of a Dyck path. St000758The length of the longest staircase fitting into an integer composition. St000759The smallest missing part in an integer partition. St000783The side length of the largest staircase partition fitting into a partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000897The number of different multiplicities of parts of an integer partition. St000917The open packing number of a graph. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St001028Number of simple modules with injective dimension equal to the dominant 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. St001194The injective dimension of $A/AfA$ in the corresponding Nakayama algebra $A$ when $Af$ is the minimal faithful projective-injective left $A$-module St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001205The number of non-simple indecomposable projective-injective modules of the algebra $eAe$ in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001244The number of simple modules of projective dimension one that are not 1-regular for the Nakayama algebra associated to a Dyck path. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001275The projective dimension of the second term in a minimal injective coresolution of the regular module. St001363The Euler characteristic of a graph according to Knill. St001432The order dimension of the partition. St001463The number of distinct columns in the nullspace of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001672The restrained domination number of a graph. St001732The number of peaks visible from the left. St001829The common independence number of a graph. St001884The number of borders of a binary word. St000025The number of initial rises of a Dyck path. St000026The position of the first return of a Dyck path. St000143The largest repeated part of a partition. St000212The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. St000297The number of leading ones in a binary word. St000326The position of the first one in a binary word after appending a 1 at the end. St000383The last part of an integer composition. St000386The number of factors DDU in a Dyck path. St000390The number of runs of ones in a binary word. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St000553The number of blocks of a graph. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000627The exponent of a binary word. St000655The length of the minimal rise of a Dyck path. St000657The smallest part of an integer composition. St000659The number of rises of length at least 2 of a Dyck path. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000733The row containing the largest entry of a standard tableau. St000745The index of the last row whose first entry is the row number in a standard Young tableau. St000762The sum of the positions of the weak records of an integer composition. St000763The sum of the positions of the strong records of an integer composition. St000764The number of strong records in an integer composition. St000765The number of weak records in an integer composition. St000781The number of proper colouring schemes of a Ferrers diagram. St000805The number of peaks of the associated bargraph. St000847The number of standard Young tableaux whose descent set is the binary word. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000913The number of ways to refine the partition into singletons. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St001031The height of the bicoloured Motzkin path associated with the Dyck path. St001035The convexity degree of the parallelogram polyomino associated with the Dyck path. St001038The minimal height of a column in the parallelogram polyomino associated with the Dyck path. St001092The number of distinct even parts of a partition. St001121The multiplicity of the irreducible representation indexed by the partition in the Kronecker square corresponding to the partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001256Number of simple reflexive modules that are 2-stable reflexive. St001280The number of parts of an integer partition that are at least two. St001340The cardinality of a minimal non-edge isolating set of a graph. St001352The number of internal nodes in the modular decomposition of a graph. St001385The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition. St001481The minimal height of a peak of a Dyck path. St001484The number of singletons of an integer partition. St001498The normalised height of a Nakayama algebra with magnitude 1. St001571The Cartan determinant of the integer partition. St001673The degree of asymmetry of an integer composition. St001691The number of kings in a graph. St001722The number of minimal chains with small intervals between a binary word and the top element. 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. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000091The descent variation of a composition. St000149The number of cells of the partition whose leg is zero and arm is odd. 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. St000290The major index of a binary word. St000291The number of descents of a binary word. St000293The number of inversions of a binary word. St000296The length of the symmetric border of a binary word. St000312The number of leaves in a graph. St000347The inversion sum of a binary word. St000531The leading coefficient of the rook polynomial of an integer partition. St000629The defect of a binary word. St000687The dimension of $Hom(I,P)$ for the LNakayama algebra of a Dyck path. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St000761The number of ascents in an integer composition. St000768The number of peaks in an integer composition. St000790The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. St000791The number of pairs of left tunnels, one strictly containing the other, of a Dyck path. St000807The sum of the heights of the valleys of the associated bargraph. St000875The semilength of the longest Dyck word in the Catalan factorisation of a binary word. St000921The number of internal inversions of a binary word. St000934The 2-degree of an integer partition. St000980The number of boxes weakly below the path and above the diagonal that lie below at least two peaks. St001057The Grundy value of the game of creating an independent set in a graph. St001107The number of times one can erase the first up and the last down step in a Dyck path and still remain a Dyck path. St001125The number of simple modules that satisfy the 2-regular condition in the corresponding Nakayama algebra. St001137Number of simple modules that are 3-regular in the corresponding Nakayama algebra. St001139The number of occurrences of hills of size 2 in a Dyck path. St001141The number of occurrences of hills of size 3 in a Dyck path. St001175The size of a partition minus the hook length of the base cell. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001264The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of 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. St001306The number of induced paths on four vertices in a graph. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001353The number of prime nodes in the modular decomposition of a graph. St001356The number of vertices in prime modules of a graph. St001371The length of the longest Yamanouchi prefix of a binary word. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001436The index of a given binary word in the lex-order among all its cyclic shifts. St001479The number of bridges of a graph. St001485The modular major index of a binary word. St001593This is the number of standard Young tableaux of the given shifted shape. St001657The number of twos in an integer partition. St001695The natural comajor index of a standard Young tableau. St001696The natural major 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. St001939The number of parts that are equal to their multiplicity in the integer partition. St001940The number of distinct parts that are equal to their multiplicity in the integer partition. St000258The burning number of a graph. St000918The 2-limited packing number of a graph. St000916The packing number of a graph. St001694The number of maximal dissociation sets in a graph. St001740The number of graphs with the same symmetric edge polytope as the given graph. St000552The number of cut vertices of a graph. St001826The maximal number of leaves on a vertex of a graph. St001315The dissociation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001588The number of distinct odd parts smaller than the largest even part in an integer partition.