searching the database
Your data matches 117 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St001701
St001701: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
=> 1
['A',2]
=> 2
['B',2]
=> 2
['G',2]
=> 2
['A',3]
=> 4
Description
The maximum down-degree of the Hasse diagram of the strong Bruhat order in the Weyl group of the Cartan type.
Matching statistic: St001788
St001788: Finite Cartan types ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
=> 2 = 1 + 1
['A',2]
=> 3 = 2 + 1
['B',2]
=> 3 = 2 + 1
['G',2]
=> 3 = 2 + 1
['A',3]
=> 5 = 4 + 1
Description
The number of types of parabolic subgroups of the associated Weyl group.
Let $W$ be a Weyl group with simple generators $\mathcal{S} \subseteq W$. A subgroup of $W$ generated by a subset $X \subseteq \mathcal{S}$ is called standard parabolic subgroup. A parabolic subgroup is a subgroup of $W$ that is conjugate to a standard parabolic subgroup.
This is the number of all pairwise different types of subgroups of $W$ obtained as (standard) parabolic subgroups (including type $A_0$).
Matching statistic: St000071
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000071: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000071: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
=> ([],1)
=> 1
['A',2]
=> ([(0,2),(1,2)],3)
=> 2
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> 2
['G',2]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> 2
['A',3]
=> ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
Description
The number of maximal chains in a poset.
Matching statistic: St000909
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00148: Finite Cartan types —to root poset⟶ Posets
St000909: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000909: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
['A',1]
=> ([],1)
=> 1
['A',2]
=> ([(0,2),(1,2)],3)
=> 2
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> 2
['G',2]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> 2
['A',3]
=> ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> 4
Description
The number of maximal chains of maximal size in a poset.
Matching statistic: St000299
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
['A',1]
=> ([],1)
=> ([],1)
=> 1
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 2
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 2
['G',2]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([(4,5)],6)
=> 2
['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)
=> 4
Description
The number of nonisomorphic vertex-induced subtrees.
Matching statistic: St000363
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
['A',1]
=> ([],1)
=> ([],1)
=> 1
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 2
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 2
['G',2]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([(4,5)],6)
=> 2
['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)
=> 4
Description
The number of minimal vertex covers of a graph.
A '''vertex cover''' of a graph $G$ is a subset $S$ of the vertices of $G$ such that each edge of $G$ contains at least one vertex of $S$. A vertex cover is minimal if it contains the least possible number of vertices.
This is also the leading coefficient of the clique polynomial of the complement of $G$.
This is also the number of independent sets of maximal cardinality of $G$.
Matching statistic: St000388
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
['A',1]
=> ([],1)
=> ([],1)
=> 1
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 2
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 2
['G',2]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([(4,5)],6)
=> 2
['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)
=> 4
Description
The number of orbits of vertices of a graph under automorphisms.
Matching statistic: St001093
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
['A',1]
=> ([],1)
=> ([],1)
=> 1
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 2
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 2
['G',2]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([(4,5)],6)
=> 2
['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)
=> 4
Description
The detour number of a graph.
This is the number of vertices in a longest induced path in a graph.
Note that [1] defines the detour number as the number of edges in a longest induced path, which is unsuitable for the empty graph.
Matching statistic: St001108
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
['A',1]
=> ([],1)
=> ([],1)
=> 1
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 2
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 2
['G',2]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([(4,5)],6)
=> 2
['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)
=> 4
Description
The 2-dynamic chromatic number of a graph.
A $k$-dynamic coloring of a graph $G$ is a proper coloring of $G$ in such a way that each vertex $v$ sees at least $\min\{d(v), k\}$ colors in its neighborhood. The $k$-dynamic chromatic number of a graph is the smallest number of colors needed to find an $k$-dynamic coloring.
This statistic records the $2$-dynamic chromatic number of a graph.
Matching statistic: St001304
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
['A',1]
=> ([],1)
=> ([],1)
=> 1
['A',2]
=> ([(0,2),(1,2)],3)
=> ([(1,2)],3)
=> 2
['B',2]
=> ([(0,3),(1,3),(3,2)],4)
=> ([(2,3)],4)
=> 2
['G',2]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ([(4,5)],6)
=> 2
['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)
=> 4
Description
The number of maximally independent sets of vertices of a graph.
An '''independent set''' of vertices of a graph is a set of vertices no two of which are adjacent. If a set of vertices is independent then so is every subset. This statistic counts the number of maximally independent sets of vertices.
The following 107 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001963The tree-depth of a graph. St000171The degree of the graph. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000362The size of a minimal vertex cover of a graph. St000537The cutwidth of a graph. St000547The number of even non-empty partial sums of an integer partition. St001176The size of a partition minus its first part. St001214The aft of an integer partition. St001440The number of standard Young tableaux whose major index is congruent one modulo the size of a given integer partition. St001512The minimum rank of a graph. 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. St001742The difference of the maximal and the minimal degree in a graph. St001961The sum of the greatest common divisors of all pairs of parts. St000208Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer partition weight. St000378The diagonal inversion number of an integer partition. St000511The number of invariant subsets when acting with a permutation of given cycle type. St000738The first entry in the last row of a standard tableau. St000935The number of ordered refinements of an integer partition. St001119The length of a shortest maximal path in a graph. St001286The annihilation number of a graph. St001302The number of minimally dominating sets of vertices of a graph. St001315The dissociation number of a graph. St001463The number of distinct columns in the nullspace of a graph. St001725The harmonious chromatic 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. St001814The number of partitions interlacing the given partition. St000228The size of a partition. St000394The sum of the heights of the peaks of a Dyck path minus the number of peaks. St000459The hook length of the base cell of a partition. St000548The number of different non-empty partial sums of an integer partition. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001104The number of descents of the invariant in a tensor power of the adjoint representation of the rank two general linear group. St001117The game chromatic index of a graph. St001215Let X be the direct sum of all simple modules of the corresponding Nakayama algebra. St001265The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra. St001692The number of vertices with higher degree than the average degree in a graph. St001712The number of natural descents of a standard Young tableau. St001792The arboricity of a graph. St000910The number of maximal chains of minimal length in a poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St000146The Andrews-Garvan crank of a partition. St000159The number of distinct parts of the integer partition. St000278The size of the preimage of the map 'to partition' from Integer compositions to Integer partitions. St000307The number of rowmotion orbits of a poset. St000346The number of coarsenings of a partition. St000473The number of parts of a partition that are strictly bigger than the number of ones. St000533The minimum of the number of parts and the size of the first part of an integer partition. St000783The side length of the largest staircase partition fitting into a partition. St000810The sum of the entries in the column specified by the partition of the change of basis matrix from powersum symmetric functions to monomial symmetric functions. St001105The number of greedy linear extensions of a poset. St001106The number of supergreedy linear extensions of a poset. St001330The hat guessing number of a graph. St001432The order dimension of the partition. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000318The number of addable cells of the Ferrers diagram of an integer partition. St000454The largest eigenvalue of a graph if it is integral. St000481The number of upper covers of a partition in dominance order. St001118The acyclic chromatic index of a graph. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St001644The dimension of a graph. St000143The largest repeated part of a partition. St000183The side length of the Durfee square of an integer partition. St000668The least common multiple of the parts of the partition. St000755The number of real roots of the characteristic polynomial of a linear recurrence associated with an integer partition. St001128The exponens consonantiae of a partition. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000207Number of integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000456The monochromatic index of a connected graph. St000460The hook length of the last cell along the main diagonal of an integer partition. St000480The number of lower covers of a partition in dominance order. St000759The smallest missing part in an integer partition. St000870The product of the hook lengths of the diagonal cells in an integer partition. St001092The number of distinct even parts of a partition. St001380The number of monomer-dimer tilings of a Ferrers diagram. St001480The number of simple summands of the module J^2/J^3. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001627The number of coloured connected graphs such that the multiplicities of colours are given by a partition. St001638The book thickness of a graph. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001924The number of cells in an integer partition whose arm and leg length coincide. St000477The weight of a partition according to Alladi. St000478Another weight of a partition according to Alladi. St001248Sum of the even parts of a partition. St001279The sum of the parts of an integer partition that are at least two. St001541The Gini index of an integer partition. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000455The second largest eigenvalue of a graph if it is integral. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000310The minimal degree of a vertex of a graph. St000450The number of edges minus the number of vertices plus 2 of a graph. St000741The Colin de Verdière graph invariant. St001642The Prague dimension of a graph. St001734The lettericity of a graph. St001812The biclique partition number of a graph. St000095The number of triangles of a graph. St000286The number of connected components of the complement of a graph. St000303The determinant of the product of the incidence matrix and its transpose of a graph divided by $4$. St000822The Hadwiger number of the 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. St001575The minimal number of edges to add or remove to make a graph edge transitive.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!