- FindStat

Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001110
(load all 2 compositions to match this statistic)

Mapping

Mp00160: Permutations —graph of inversions⟶ Graphs
St001110: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1] => ([],1)
 => 1
[1,2] => ([],2)
 => 1
[2,1] => ([(0,1)],2)
 => 2
[1,2,3] => ([],3)
 => 1
[1,3,2] => ([(1,2)],3)
 => 2
[2,1,3] => ([(1,2)],3)
 => 2
[2,3,1] => ([(0,2),(1,2)],3)
 => 3
[3,1,2] => ([(0,2),(1,2)],3)
 => 3
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 3
[1,2,3,4] => ([],4)
 => 1
[1,2,4,3] => ([(2,3)],4)
 => 2
[1,3,2,4] => ([(2,3)],4)
 => 2
[1,3,4,2] => ([(1,3),(2,3)],4)
 => 3
[1,4,2,3] => ([(1,3),(2,3)],4)
 => 3
[1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => 3
[2,1,3,4] => ([(2,3)],4)
 => 2
[2,1,4,3] => ([(0,3),(1,2)],4)
 => 2
[2,3,1,4] => ([(1,3),(2,3)],4)
 => 3
[2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => 4
[2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 3
[2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[3,1,2,4] => ([(1,3),(2,3)],4)
 => 3
[3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 3
[3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => 3
[3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 4
[4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[1,2,3,4,5] => ([],5)
 => 1
[1,2,3,5,4] => ([(3,4)],5)
 => 2
[1,2,4,3,5] => ([(3,4)],5)
 => 2
[1,2,4,5,3] => ([(2,4),(3,4)],5)
 => 3
[1,2,5,3,4] => ([(2,4),(3,4)],5)
 => 3
[1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => 3
[1,3,2,4,5] => ([(3,4)],5)
 => 2
[1,3,2,5,4] => ([(1,4),(2,3)],5)
 => 2
[1,3,4,2,5] => ([(2,4),(3,4)],5)
 => 3
[1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
 => 4
[1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
 => 3
[1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,4,2,3,5] => ([(2,4),(3,4)],5)
 => 3
[1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
 => 3
[1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => 3
[1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4

Description

The 3-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

$3$ -dynamic chromatic number of a graph.

Matching statistic: St001207
(load all 46 compositions to match this statistic)

Mapping

St001207: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 57%

Values

[1] => ? = 1 - 1
[1,2] => 0 = 1 - 1
[2,1] => 1 = 2 - 1
[1,2,3] => 0 = 1 - 1
[1,3,2] => 1 = 2 - 1
[2,1,3] => 1 = 2 - 1
[2,3,1] => 2 = 3 - 1
[3,1,2] => 2 = 3 - 1
[3,2,1] => 2 = 3 - 1
[1,2,3,4] => 0 = 1 - 1
[1,2,4,3] => 1 = 2 - 1
[1,3,2,4] => 1 = 2 - 1
[1,3,4,2] => 2 = 3 - 1
[1,4,2,3] => 2 = 3 - 1
[1,4,3,2] => 2 = 3 - 1
[2,1,3,4] => 1 = 2 - 1
[2,1,4,3] => 1 = 2 - 1
[2,3,1,4] => 2 = 3 - 1
[2,3,4,1] => 3 = 4 - 1
[2,4,1,3] => 2 = 3 - 1
[2,4,3,1] => 3 = 4 - 1
[3,1,2,4] => 2 = 3 - 1
[3,1,4,2] => 2 = 3 - 1
[3,2,1,4] => 2 = 3 - 1
[3,2,4,1] => 3 = 4 - 1
[3,4,1,2] => 3 = 4 - 1
[3,4,2,1] => 3 = 4 - 1
[4,1,2,3] => 3 = 4 - 1
[4,1,3,2] => 3 = 4 - 1
[4,2,1,3] => 3 = 4 - 1
[4,2,3,1] => 3 = 4 - 1
[4,3,1,2] => 3 = 4 - 1
[4,3,2,1] => 3 = 4 - 1
[1,2,3,4,5] => ? = 1 - 1
[1,2,3,5,4] => ? = 2 - 1
[1,2,4,3,5] => ? = 2 - 1
[1,2,4,5,3] => ? = 3 - 1
[1,2,5,3,4] => ? = 3 - 1
[1,2,5,4,3] => ? = 3 - 1
[1,3,2,4,5] => ? = 2 - 1
[1,3,2,5,4] => ? = 2 - 1
[1,3,4,2,5] => ? = 3 - 1
[1,3,4,5,2] => ? = 4 - 1
[1,3,5,2,4] => ? = 3 - 1
[1,3,5,4,2] => ? = 4 - 1
[1,4,2,3,5] => ? = 3 - 1
[1,4,2,5,3] => ? = 3 - 1
[1,4,3,2,5] => ? = 3 - 1
[1,4,3,5,2] => ? = 4 - 1
[1,4,5,2,3] => ? = 4 - 1
[1,4,5,3,2] => ? = 4 - 1
[1,5,2,3,4] => ? = 4 - 1
[1,5,2,4,3] => ? = 4 - 1
[1,5,3,2,4] => ? = 4 - 1
[1,5,3,4,2] => ? = 4 - 1
[1,5,4,2,3] => ? = 4 - 1
[1,5,4,3,2] => ? = 4 - 1
[2,1,3,4,5] => ? = 2 - 1
[2,1,3,5,4] => ? = 2 - 1
[2,1,4,3,5] => ? = 2 - 1
[2,1,4,5,3] => ? = 3 - 1
[2,1,5,3,4] => ? = 3 - 1
[2,1,5,4,3] => ? = 3 - 1
[2,3,1,4,5] => ? = 3 - 1
[2,3,1,5,4] => ? = 3 - 1
[2,3,4,1,5] => ? = 4 - 1
[2,3,4,5,1] => ? = 4 - 1
[2,3,5,1,4] => ? = 4 - 1
[2,3,5,4,1] => ? = 4 - 1
[2,4,1,3,5] => ? = 3 - 1
[2,4,1,5,3] => ? = 3 - 1
[2,4,3,1,5] => ? = 4 - 1
[2,4,3,5,1] => ? = 4 - 1
[2,4,5,1,3] => ? = 4 - 1
[2,4,5,3,1] => ? = 4 - 1
[2,5,1,3,4] => ? = 4 - 1
[2,5,1,4,3] => ? = 4 - 1
[2,5,3,1,4] => ? = 4 - 1
[2,5,3,4,1] => ? = 4 - 1
[2,5,4,1,3] => ? = 4 - 1
[2,5,4,3,1] => ? = 4 - 1
[3,1,2,4,5] => ? = 3 - 1

Description

The Lowey length of the algebra

$A/T$ when

$T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of

$K[x]/(x^n)$ .