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Your data matches 290 different statistics following compositions of up to 3 maps.
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Matching statistic: St001613
Values
([],1)
=> 0 = 1 - 1
([(0,1)],2)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> 1 = 2 - 1
Description
The binary logarithm of the size of the center of a lattice.
An element of a lattice is central if it is neutral and has a complement. The subposet induced by central elements is a Boolean lattice.
Matching statistic: St001621
Values
([],1)
=> 0 = 1 - 1
([(0,1)],2)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> 1 = 2 - 1
Description
The number of atoms of a lattice.
An element of a lattice is an '''atom''' if it covers the least element.
Matching statistic: St001720
Values
([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,2),(2,1)],3)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
Description
The minimal length of a chain of small intervals in a lattice.
An interval $[a, b]$ is small if $b$ is a join of elements covering $a$.
Matching statistic: St000069
Values
([],1)
=> ([],0)
=> 0 = 1 - 1
([(0,1)],2)
=> ([],1)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> ([(0,1)],2)
=> 1 = 2 - 1
Description
The number of maximal elements of a poset.
Matching statistic: St000845
Values
([],1)
=> ([],1)
=> 0 = 1 - 1
([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 2 - 1
Description
The maximal number of elements covered by an element in a poset.
Matching statistic: St000846
Values
([],1)
=> ([],1)
=> 0 = 1 - 1
([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 2 - 1
Description
The maximal number of elements covering an element of a poset.
Matching statistic: St001942
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 0 = 1 - 1
([(0,1)],2)
=> ([(0,1)],2)
=> 1 = 2 - 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1 = 2 - 1
Description
The number of loops of the quiver corresponding to the reduced incidence algebra of a poset.
Matching statistic: St000097
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 2
Description
The order of the largest clique of the graph.
A clique in a graph $G$ is a subset $U \subseteq V(G)$ such that any pair of vertices in $U$ are adjacent. I.e. the subgraph induced by $U$ is a complete graph.
Matching statistic: St000098
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 2
Description
The chromatic number of a graph.
The minimal number of colors needed to color the vertices of the graph such that no two vertices which share an edge have the same color.
Matching statistic: St000172
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> 2
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(1,2)],3)
=> 2
Description
The Grundy number of a graph.
The Grundy number $\Gamma(G)$ is defined to be the largest $k$ such that $G$ admits a greedy $k$-coloring. Any order of the vertices of $G$ induces a greedy coloring by assigning to the $i$-th vertex in this order the smallest positive integer such that the partial coloring remains a proper coloring.
In particular, we have that $\chi(G) \leq \Gamma(G) \leq \Delta(G) + 1$, where $\chi(G)$ is the chromatic number of $G$ ([[St000098]]), and where $\Delta(G)$ is the maximal degree of a vertex of $G$ ([[St000171]]).
The following 280 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000244The cardinality of the automorphism group of a graph. St000258The burning number of a graph. St000286The number of connected components of the complement of a graph. St000364The exponent of the automorphism group of a graph. St000378The diagonal inversion number of an integer partition. St000469The distinguishing number of a graph. St000478Another weight of a partition according to Alladi. St000510The number of invariant oriented cycles when acting with a permutation of given cycle type. St000636The hull number of a graph. St000644The number of graphs with given frequency partition. St000722The number of different neighbourhoods in a graph. St000822The Hadwiger number of the graph. St000907The number of maximal antichains of minimal length in a poset. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St000939The number of characters of the symmetric group whose value on the partition is positive. St001029The size of the core of a graph. St001109The number of proper colourings of a graph with as few colours as possible. St001116The game chromatic number of a graph. St001261The Castelnuovo-Mumford regularity of a graph. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001315The dissociation number of a graph. St001316The domatic number of a graph. St001330The hat guessing number of a graph. St001366The maximal multiplicity of a degree of a vertex of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001642The Prague dimension of a graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001670The connected partition number of a graph. St001746The coalition number of a graph. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St001883The mutual visibility number of a graph. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001963The tree-depth of a graph. St000149The number of cells of the partition whose leg is zero and arm is odd. St000256The number of parts from which one can substract 2 and still get an integer partition. 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. St000362The size of a minimal vertex cover of a graph. St000387The matching number of a graph. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000480The number of lower covers of a partition in dominance order. St000535The rank-width of a graph. St000536The pathwidth of a graph. St000537The cutwidth of a graph. St000697The number of 3-rim hooks removed from an integer partition to obtain its associated 3-core. St000741The Colin de Verdière graph invariant. St000778The metric dimension of a graph. St000944The 3-degree of an integer partition. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001251The number of parts of a partition that are not congruent 1 modulo 3. St001270The bandwidth of a graph. St001271The competition number of a graph. St001277The degeneracy of a graph. St001280The number of parts of an integer partition that are at least two. St001333The cardinality of a minimal edge-isolating set of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001349The number of different graphs obtained from the given graph by removing an edge. St001354The number of series nodes in the modular decomposition of a graph. St001358The largest degree of a regular subgraph of a graph. St001393The induced matching number of a graph. St001395The number of strictly unfriendly partitions of a graph. St001644The dimension of a graph. St001743The discrepancy of a graph. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001792The arboricity of a graph. St001794Half the number of sets of vertices in a graph which are dominating and non-blocking. St001812The biclique partition number of a graph. St001912The length of the preperiod in Bulgarian solitaire corresponding to an integer partition. St001949The rigidity index of a graph. St001962The proper pathwidth of a graph. St001625The Möbius invariant of a lattice. St000006The dinv of a Dyck path. St000086The number of subgraphs. St000087The number of induced subgraphs. St000088The row sums of the character table of the symmetric group. St000093The cardinality of a maximal independent set of vertices of a graph. St000147The largest part of an integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000259The diameter of a connected graph. St000269The number of acyclic orientations of a graph. St000270The number of forests contained in a graph. St000273The domination number of a graph. St000276The size of the preimage of the map 'to graph' from Ordered trees to Graphs. St000283The size of the preimage of the map 'to graph' from Binary trees to Graphs. St000287The number of connected components of a graph. St000299The number of nonisomorphic vertex-induced subtrees. St000309The number of vertices with even degree. St000315The number of isolated vertices of a graph. St000321The number of integer partitions of n that are dominated by an integer partition. St000343The number of spanning subgraphs of a graph. St000345The number of refinements of a partition. St000363The number of minimal vertex covers of a graph. St000384The maximal part of the shifted composition of an integer partition. St000388The number of orbits of vertices of a graph under automorphisms. St000452The number of distinct eigenvalues of a graph. St000453The number of distinct Laplacian eigenvalues of a graph. St000468The Hosoya index of a graph. St000479The Ramsey number of a graph. St000482The (zero)-forcing number of a graph. St000531The leading coefficient of the rook polynomial of an integer partition. St000544The cop number of a graph. St000549The number of odd partial sums of an integer partition. St000553The number of blocks of a graph. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. 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. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St000784The maximum of the length and the largest part of the integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000916The packing number of a graph. St000926The clique-coclique number of a graph. St000935The number of ordered refinements of an integer partition. St000955Number of times one has $Ext^i(D(A),A)>0$ for $i>0$ for the corresponding LNakayama algebra. St000972The composition number of a graph. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St000992The alternating sum of the parts of an integer partition. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001093The detour number of a graph. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001111The weak 2-dynamic chromatic number of a graph. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001165Number of simple modules with even projective dimension in the corresponding Nakayama algebra. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001239The largest vector space dimension of the double dual of a simple module in the corresponding Nakayama algebra. St001257The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001286The annihilation 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. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001342The number of vertices in the center of a graph. St001352The number of internal nodes in the modular decomposition of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001363The Euler characteristic of a graph according to Knill. St001368The number of vertices of maximal degree in a graph. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001389The number of partitions of the same length below the given integer partition. St001463The number of distinct columns in the nullspace of a graph. St001471The magnitude of a Dyck path. St001474The evaluation of the Tutte polynomial of the graph at (x,y) equal to (2,-1). St001486The number of corners of the ribbon associated with an integer composition. St001488The number of corners of a skew partition. St001512The minimum rank of a graph. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules 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. St001571The Cartan determinant of the integer partition. St001600The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple graphs. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001608The number of coloured rooted trees such that the multiplicities of colours are given by a partition. St001645The pebbling number of a connected graph. St001649The length of a longest trail in a graph. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001672The restrained domination number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001691The number of kings in a graph. 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. St001716The 1-improper chromatic number of a graph. St001725The harmonious chromatic number of a graph. St001734The lettericity of a graph. St001757The number of orbits of toric promotion on a graph. St001758The number of orbits of promotion on 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. St001785The number of ways to obtain a partition as the multiset of antidiagonal lengths of the Ferrers diagram of a partition. St001802The number of endomorphisms of a graph. St001828The Euler characteristic of a graph. St001829The common independence number of a graph. St001951The number of factors in the disjoint direct product decomposition of the automorphism group of a graph. St000081The number of edges of a graph. St000120The number of left tunnels of a Dyck path. St000142The number of even parts of a partition. St000143The largest repeated part of a partition. St000145The Dyson rank of a partition. St000150The floored half-sum of the multiplicities of a partition. St000171The degree of the graph. St000257The number of distinct parts of a partition that occur at least twice. St000263The Szeged index of a graph. St000265The Wiener index of a graph. St000274The number of perfect matchings of a graph. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000329The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1. St000361The second Zagreb index of a graph. St000377The dinv defect of an integer partition. St000379The number of Hamiltonian cycles in a graph. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000386The number of factors DDU in a Dyck path. St000454The largest eigenvalue of a graph if it is integral. St000466The Gutman (or modified Schultz) index of a connected graph. St000481The number of upper covers of a partition in dominance order. St000513The number of invariant subsets of size 2 when acting with a permutation of given cycle type. St000547The number of even non-empty partial sums of an integer partition. St000552The number of cut vertices of a graph. St000659The number of rises of length at least 2 of a Dyck path. St000688The global dimension minus the dominant dimension of the LNakayama algebra associated to a Dyck path. St000941The number of characters of the symmetric group whose value on the partition is even. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001011Number of simple modules of projective dimension 2 in the Nakayama algebra corresponding to the Dyck path. St001012Number of simple modules with projective dimension at most 2 in the Nakayama algebra corresponding to the Dyck path. St001026The maximum of the projective dimensions of the indecomposable non-projective injective modules minus the minimum in the Nakayama algebra corresponding to the Dyck path. St001031The height of the bicoloured Motzkin path associated with 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. St001056The Grundy value for the game of deleting vertices of a graph until it has no edges. St001071The beta invariant of the graph. St001092The number of distinct even parts of a partition. St001117The game chromatic index of a graph. St001179Number of indecomposable injective modules with projective dimension at most 2 in the corresponding Nakayama algebra. St001183The maximum of $projdim(S)+injdim(S)$ over all simple modules in the Nakayama algebra corresponding to the Dyck path. St001185The number of indecomposable injective modules of grade at least 2 in the corresponding Nakayama algebra. 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. St001192The maximal dimension of $Ext_A^2(S,A)$ for a simple module $S$ over the corresponding Nakayama algebra $A$. St001212The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group with the regular module. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001217The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1. St001222Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension 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. St001252Half the sum of the even parts of a partition. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001273The projective dimension of the first term in an injective coresolution of the regular module. St001331The size of the minimal feedback vertex set. St001335The cardinality of a minimal cycle-isolating set of a graph. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001341The number of edges in the center of a graph. St001345The Hamming dimension of a graph. St001347The number of pairs of vertices of a graph having the same neighbourhood. St001362The normalized Knill dimension of a graph. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001391The disjunction number of a graph. St001418Half of the global dimension of the stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001424The number of distinct squares in a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001458The rank of the adjacency matrix of a graph. St001479The number of bridges of a graph. St001502The global dimension minus the dominant dimension of magnitude 1 Nakayama algebras. St001507The sum of projective dimension of simple modules with even projective dimension divided by 2 in the LNakayama algebra corresponding to Dyck paths. St001508The degree of the standard monomial associated to a Dyck path relative to the diagonal boundary. St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. 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. St001587Half of the largest even part of an integer partition. St001638The book thickness of a graph. St001657The number of twos in an integer partition. St001689The number of celebrities in a graph. St001692The number of vertices with higher degree than the average degree in a graph. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001730The number of times the path corresponding to a binary word crosses the base line. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001777The number of weak descents in an integer composition. St001783The number of odd automorphisms of a graph. St001826The maximal number of leaves on a vertex of a graph. St001827The number of two-component spanning forests of a graph. St001869The maximum cut size of a graph. 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). St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St001931The weak major index of an integer composition regarded as a word. St000351The determinant of the adjacency matrix of a graph. St000455The second largest eigenvalue of a graph if it is integral.
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