Your data matches 220 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000139
Mapping
St000139: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 3 = 2 + 1
['B',2]
 => 4 = 3 + 1
['A',3]
 => 4 = 3 + 1
Description
The Coxeter number of a finite Cartan type. The Coxeter number $h$ for the Weyl group $W$ of the given finite Cartan type is defined as the order of the product of the Coxeter generators of $W$. Equivalently, this is equal to the maximal degree of a fundamental invariant of $W$, see also [[St000138]].
Matching statistic: St001150
Mapping
St001150: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 3 = 2 + 1
['B',2]
 => 4 = 3 + 1
['A',3]
 => 4 = 3 + 1
Description
The minimal dimension of a faithful linear representation of the Lie algebra of given type.
Matching statistic: St001495
Mapping
St001495: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 3 = 2 + 1
['B',2]
 => 4 = 3 + 1
['A',3]
 => 4 = 3 + 1
Description
The maximal order of an element in the Weyl group of a given Cartan type. For the symmetric group, this is [[oeis:A000793]]
Matching statistic: St001897
Mapping
St001897: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 3 = 2 + 1
['B',2]
 => 4 = 3 + 1
['A',3]
 => 4 = 3 + 1
Description
The minimal degree of a faithful permutation representation of a Weyl group. Data are from [1, Table 1].
Matching statistic: St001950
Mapping
St001950: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => 1 = 2 - 1
['B',2]
 => 2 = 3 - 1
['A',3]
 => 2 = 3 - 1
Description
The minimal size of a base for the Weyl group of the Cartan type. A base of a permutation group is a set $B$ such that the pointwise stabilizer of $B$ is trivial. For example, a base of the symmetric group on $n$ letters must contain all but one letter. Any base has at least $\log |G|/n$ elements, where $n$ is the degree of the group, i.e., the size of its domain.
Matching statistic: St000528
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000528: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => 2
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 3
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 3
Description
The height of a poset. This equals the rank of the poset [[St000080]] plus one.
Matching statistic: St000906
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000906: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => 2
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 3
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 3
Description
The length of the shortest maximal chain in a poset.
Matching statistic: St000080
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000080: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => 1 = 2 - 1
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => 2 = 3 - 1
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => 2 = 3 - 1
Description
The rank of the poset.
Matching statistic: St000093
(load all 2 compositions to match this statistic)
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00198: Posets —incomparability graph⟶ Graphs
St000093: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => ([(1,2)],3)
 => 2
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(2,3)],4)
 => 3
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 3
Description
The cardinality of a maximal independent set of vertices of a graph. An independent set of a graph is a set of pairwise non-adjacent vertices. A maximum independent set is an independent set of maximum cardinality. This statistic is also called the independence number or stability number $\alpha(G)$ of $G$.
Matching statistic: St000147
Mapping
Mp00148: Finite Cartan types —to root poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
St000147: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',2]
 => ([(0,2),(1,2)],3)
 => [2,1]
 => 2
['B',2]
 => ([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => 3
['A',3]
 => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,2,1]
 => 3
Description
The largest part of an integer partition.
The following 210 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000171The degree of the graph. St000258The burning number of a graph. St000271The chromatic index of a graph. St000273The domination number of a graph. St000384The maximal part of the shifted composition of an integer partition. St000482The (zero)-forcing number of a graph. St000544The cop number of a graph. St000553The number of blocks of a 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. St001112The 3-weak dynamic number of a graph. St001118The acyclic chromatic index 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. St001345The Hamming dimension of a graph. St001622The number of join-irreducible elements of a lattice. St001626The number of maximal proper sublattices of a lattice. St001642The Prague dimension of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001704The size of the largest multi-subset-intersection of the deck of a graph with the deck of another graph. St001720The minimal length of a chain of small intervals in a lattice. St001829The common independence number of a graph. St001883The mutual visibility number of a graph. St000148The number of odd parts of a partition. St000225Difference between largest and smallest parts in a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000537The cutwidth of a graph. St000636The hull number of a graph. St000680The Grundy value for Hackendot on posets. St000776The maximal multiplicity of an eigenvalue in a graph. St000778The metric dimension of a graph. St000785The number of distinct colouring schemes of a graph. St000918The 2-limited packing number of a graph. St000937The number of positive values of the symmetric group character corresponding to the partition. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St000992The alternating sum of the parts of an integer partition. St001110The 3-dynamic chromatic number of a graph. St001247The number of parts of a partition that are not congruent 2 modulo 3. St001270The bandwidth of a graph. St001315The dissociation number of a graph. St001323The independence gap of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001385The number of conjugacy classes of subgroups with connected subgroups of sizes prescribed by an integer partition. St001463The number of distinct columns in the nullspace of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St001593This is the number of standard Young tableaux of the given shifted shape. St001606The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on set partitions. St001644The dimension of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001723The differential of a graph. St001724The 2-packing differential of a graph. St001742The difference of the maximal and the minimal degree in a graph. St001746The coalition number of a graph. St001820The size of the image of the pop stack sorting operator. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St001949The rigidity index of a graph. St001962The proper pathwidth of a graph. St000550The number of modular elements of a lattice. St000551The number of left modular elements of a lattice. St000752The Grundy value for the game 'Couples are forever' on an integer partition. St001057The Grundy value of the game of creating an independent set in a graph. St001638The book thickness of a graph. St001767The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. St001625The Möbius invariant of a lattice. St000010The length of the partition. St000015The number of peaks of a Dyck path. St000097The order of the largest clique of the graph. St000098The chromatic number of a graph. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000645The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between. St000676The number of odd rises of a Dyck path. St000734The last entry in the first row of a standard tableau. St000822The Hadwiger number of the graph. St000907The number of maximal antichains of minimal length in a poset. St000916The packing number of a graph. St001029The size of the core of a graph. St001039The maximal height of a column in the parallelogram polyomino associated with a Dyck path. St001068Number of torsionless simple modules in the corresponding Nakayama algebra. St001119The length of a shortest maximal path in a graph. 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 $eA$. 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: St001225The vector space dimension of the first extension group between J and itself when J is the Jacobson radical of the corresponding Nakayama algebra. St001278The number of indecomposable modules that are fixed by $\tau \Omega^1$ composed with its inverse in the corresponding Nakayama algebra. St001286The annihilation number of a graph. St001316The domatic number of a graph. St001494The Alon-Tarsi number of a graph. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001580The acyclic chromatic number of a graph. St001654The monophonic hull number of a graph. St001914The size of the orbit of an integer partition in Bulgarian solitaire. St001955The number of natural descents for set-valued two row standard Young tableaux. St000053The number of valleys of the Dyck path. St000120The number of left tunnels of a Dyck path. St000144The pyramid weight of the Dyck path. St000159The number of distinct parts of the integer partition. St000160The multiplicity of the smallest part of a partition. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000272The treewidth of a graph. St000288The number of ones in a binary word. St000299The number of nonisomorphic vertex-induced subtrees. St000306The bounce count of a Dyck path. St000309The number of vertices with even degree. St000310The minimal degree of a vertex of a graph. St000313The number of degree 2 vertices of a graph. St000331The number of upper interactions of a Dyck path. St000376The bounce deficit of a Dyck path. St000377The dinv defect of an integer partition. St000393The number of strictly increasing runs in a binary word. St000445The number of rises of length 1 of a Dyck path. St000459The hook length of the base cell of a partition. St000512The number of invariant subsets of size 3 when acting with a permutation of given cycle type. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000536The pathwidth of a graph. St000549The number of odd partial sums of an integer partition. St000631The number of distinct palindromic decompositions of a binary word. St000706The product of the factorials of the multiplicities of an integer partition. St000744The length of the path to the largest entry in a standard Young tableau. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St000783The side length of the largest staircase partition fitting into a partition. St000917The open packing number of a graph. St000922The minimal number such that all substrings of this length are unique. St000970Number of peaks minus the dominant dimension of the corresponding LNakayama algebra. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001020Sum of the codominant dimensions of the non-projective indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path. St001028Number of simple modules with injective dimension equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001034The 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. St001142The projective dimension of the socle of the regular module as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001169Number of simple modules with projective dimension at least two in the corresponding Nakayama algebra. 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. 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. St001197The global dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001199The dominant 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 $eA$. St001211The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module. St001258Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra. St001267The length of the Lyndon factorization of the binary word. St001277The degeneracy of a graph. St001291The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path. 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. St001348The bounce of the parallelogram polyomino associated with the Dyck path. St001358The largest degree of a regular subgraph of a graph. St001372The length of a longest cyclic run of ones of a binary word. St001432The order dimension of the partition. St001437The flex of a binary word. St001491The number of indecomposable projective-injective modules in the algebra corresponding to a subset. St001492The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra. St001499The number of indecomposable projective-injective modules of a magnitude 1 Nakayama algebra. St001505The number of elements generated by the Dyck path as a map in the full transformation monoid. St001509The degree of the standard monomial associated to a Dyck path relative to the trivial lower boundary. St001571The Cartan determinant of the integer partition. St001672The restrained domination number of a graph. St001716The 1-improper chromatic number of a graph. St001743The discrepancy of a graph. St001792The arboricity of a graph. St001816Eigenvalues of the top-to-random operator acting on a simple module. St001875The number of simple modules with projective dimension at most 1. St001884The number of borders of a binary word. St001924The number of cells in an integer partition whose arm and leg length coincide. St001933The largest multiplicity of a part in an integer partition. St000142The number of even parts of a partition. St000149The number of cells of the partition whose leg is zero and arm is odd. St000150The floored half-sum of the multiplicities of a partition. St000256The number of parts from which one can substract 2 and still get an integer partition. St000257The number of distinct parts of a partition that occur at least twice. St000295The length of the border of a binary word. St000379The number of Hamiltonian cycles in a graph. St000480The number of lower covers of a partition in dominance order. St000481The number of upper covers of a partition in dominance order. St000506The number of standard desarrangement tableaux of shape equal to the given partition. St000547The number of even non-empty partial sums of an integer partition. St000618The number of self-evacuating tableaux of given shape. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000671The maximin edge-connectivity for choosing a subgraph. St000998Number of indecomposable projective modules with injective dimension smaller than or equal to the dominant dimension in the Nakayama algebra corresponding to the Dyck path. St001027Number of simple modules with projective dimension equal to injective dimension in the Nakayama algebra corresponding to the Dyck path. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001071The beta invariant of the graph. St001091The number of parts in an integer partition whose next smaller part has the same size. 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. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001190Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra. St001214The aft of an integer partition. St001237The number of simple modules with injective dimension at most one or dominant dimension at least one. St001240The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra St001251The number of parts of a partition that are not congruent 1 modulo 3. St001255The vector space dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J. St001280The number of parts of an integer partition that are at least two. 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. St001364The number of permutations whose cube equals a fixed permutation of given cycle type. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001524The degree of symmetry of a binary word. St001578The minimal number of edges to add or remove to make a graph a line graph. St001650The order of Ringel's homological bijection associated to the linear Nakayama algebra corresponding to the Dyck path. St001651The Frankl number of a lattice. St001930The weak major index of a binary word. St001383The BG-rank of an integer partition.