searching the database
Your data matches 21 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: St000806
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St000806: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
St000806: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,3,2] => 10 => [1,1] => [2] => 3
[2,1,3] => 01 => [1,1] => [2] => 3
[1,2,4,3] => 110 => [2,1] => [1,1] => 3
[1,3,2,4] => 101 => [1,1,1] => [3] => 4
[1,3,4,2] => 100 => [1,2] => [1,1] => 3
[1,4,2,3] => 100 => [1,2] => [1,1] => 3
[1,4,3,2] => 100 => [1,2] => [1,1] => 3
[2,1,3,4] => 011 => [1,2] => [1,1] => 3
[2,1,4,3] => 010 => [1,1,1] => [3] => 4
[2,3,1,4] => 001 => [2,1] => [1,1] => 3
[3,1,2,4] => 001 => [2,1] => [1,1] => 3
[3,2,1,4] => 001 => [2,1] => [1,1] => 3
[1,2,3,5,4] => 1110 => [3,1] => [1,1] => 3
[1,2,4,3,5] => 1101 => [2,1,1] => [1,2] => 4
[1,2,4,5,3] => 1100 => [2,2] => [2] => 3
[1,2,5,3,4] => 1100 => [2,2] => [2] => 3
[1,2,5,4,3] => 1100 => [2,2] => [2] => 3
[1,3,2,4,5] => 1011 => [1,1,2] => [2,1] => 4
[1,3,2,5,4] => 1010 => [1,1,1,1] => [4] => 5
[1,3,4,2,5] => 1001 => [1,2,1] => [1,1,1] => 4
[1,3,4,5,2] => 1000 => [1,3] => [1,1] => 3
[1,3,5,2,4] => 1000 => [1,3] => [1,1] => 3
[1,3,5,4,2] => 1000 => [1,3] => [1,1] => 3
[1,4,2,3,5] => 1001 => [1,2,1] => [1,1,1] => 4
[1,4,2,5,3] => 1000 => [1,3] => [1,1] => 3
[1,4,3,2,5] => 1001 => [1,2,1] => [1,1,1] => 4
[1,4,3,5,2] => 1000 => [1,3] => [1,1] => 3
[1,4,5,2,3] => 1000 => [1,3] => [1,1] => 3
[1,4,5,3,2] => 1000 => [1,3] => [1,1] => 3
[1,5,2,3,4] => 1000 => [1,3] => [1,1] => 3
[1,5,2,4,3] => 1000 => [1,3] => [1,1] => 3
[1,5,3,2,4] => 1000 => [1,3] => [1,1] => 3
[1,5,3,4,2] => 1000 => [1,3] => [1,1] => 3
[1,5,4,2,3] => 1000 => [1,3] => [1,1] => 3
[1,5,4,3,2] => 1000 => [1,3] => [1,1] => 3
[2,1,3,4,5] => 0111 => [1,3] => [1,1] => 3
[2,1,3,5,4] => 0110 => [1,2,1] => [1,1,1] => 4
[2,1,4,3,5] => 0101 => [1,1,1,1] => [4] => 5
[2,1,4,5,3] => 0100 => [1,1,2] => [2,1] => 4
[2,1,5,3,4] => 0100 => [1,1,2] => [2,1] => 4
[2,1,5,4,3] => 0100 => [1,1,2] => [2,1] => 4
[2,3,1,4,5] => 0011 => [2,2] => [2] => 3
[2,3,1,5,4] => 0010 => [2,1,1] => [1,2] => 4
[2,3,4,1,5] => 0001 => [3,1] => [1,1] => 3
[2,4,1,3,5] => 0001 => [3,1] => [1,1] => 3
[2,4,3,1,5] => 0001 => [3,1] => [1,1] => 3
[3,1,2,4,5] => 0011 => [2,2] => [2] => 3
[3,1,2,5,4] => 0010 => [2,1,1] => [1,2] => 4
[3,1,4,2,5] => 0001 => [3,1] => [1,1] => 3
[3,2,1,4,5] => 0011 => [2,2] => [2] => 3
Description
The semiperimeter of the associated bargraph.
Interpret the composition as the sequence of heights of the bars of a bargraph. This statistic is the semiperimeter of the polygon determined by the axis and the bargraph. Put differently, it is the sum of the number of up steps and the number of horizontal steps when regarding the bargraph as a path with up, horizontal and down steps.
Matching statistic: St000483
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
St000483: Permutations ⟶ ℤResult quality: 64% ●values known / values provided: 64%●distinct values known / distinct values provided: 75%
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
St000483: Permutations ⟶ ℤResult quality: 64% ●values known / values provided: 64%●distinct values known / distinct values provided: 75%
Values
[1,3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 1 = 3 - 2
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 1 = 3 - 2
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1 = 3 - 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 2 = 4 - 2
[1,3,4,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 1 = 3 - 2
[1,4,2,3] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 1 = 3 - 2
[1,4,3,2] => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 1 = 3 - 2
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1 = 3 - 2
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2 = 4 - 2
[2,3,1,4] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 1 = 3 - 2
[3,1,2,4] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 1 = 3 - 2
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 1 = 3 - 2
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 1 = 3 - 2
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 2 = 4 - 2
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 1 = 3 - 2
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 1 = 3 - 2
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 1 = 3 - 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2 = 4 - 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 3 = 5 - 2
[1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 2 = 4 - 2
[1,3,4,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,3,5,2,4] => [1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,3,5,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,4,2,3,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 2 = 4 - 2
[1,4,2,5,3] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 2 = 4 - 2
[1,4,3,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,4,5,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,5,2,3,4] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,5,2,4,3] => [1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,5,3,2,4] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,5,4,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 1 = 3 - 2
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1 = 3 - 2
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 2 = 4 - 2
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 3 = 5 - 2
[2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => 2 = 4 - 2
[2,1,5,3,4] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => 2 = 4 - 2
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => 2 = 4 - 2
[2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 1 = 3 - 2
[2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 2 = 4 - 2
[2,3,4,1,5] => [4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1 = 3 - 2
[2,4,1,3,5] => [3,4,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1 = 3 - 2
[2,4,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1 = 3 - 2
[3,1,2,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 1 = 3 - 2
[3,1,2,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => 2 = 4 - 2
[3,1,4,2,5] => [4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1 = 3 - 2
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 1 = 3 - 2
[1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => ? = 3 - 2
[1,2,3,4,7,5,6] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => ? = 3 - 2
[1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => ? = 3 - 2
[1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => ? = 4 - 2
[1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => ? = 5 - 2
[1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => ? = 4 - 2
[1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,5,7,4,6] => [1,2,3,6,7,4,5] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,5,7,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,6,4,5,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => ? = 4 - 2
[1,2,3,6,4,7,5] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => ? = 4 - 2
[1,2,3,6,5,7,4] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,6,7,4,5] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,6,7,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,7,4,5,6] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,7,4,6,5] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,7,5,4,6] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,7,6,4,5] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3 - 2
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => ? = 4 - 2
[1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => ? = 5 - 2
[1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => ? = 6 - 2
[1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => ? = 5 - 2
[1,2,4,3,7,5,6] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => ? = 5 - 2
[1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => ? = 5 - 2
[1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => ? = 4 - 2
[1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => ? = 4 - 2
[1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => ? = 4 - 2
[1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,5,7,3,6] => [1,2,6,4,7,3,5] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,5,7,6,3] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,6,3,5,7] => [1,2,5,6,3,4,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => ? = 4 - 2
[1,2,4,6,3,7,5] => [1,2,5,7,3,6,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,6,5,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => ? = 4 - 2
[1,2,4,6,5,7,3] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,6,7,3,5] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,6,7,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,7,3,5,6] => [1,2,5,7,3,6,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,7,3,6,5] => [1,2,5,7,3,6,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,7,5,3,6] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,7,5,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,7,6,3,5] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,4,7,6,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,5,3,4,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => ? = 4 - 2
[1,2,5,3,4,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => ? = 4 - 2
[1,2,5,3,6,4,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => ? = 4 - 2
[1,2,5,3,6,7,4] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
[1,2,5,3,7,4,6] => [1,2,6,4,7,3,5] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => ? = 3 - 2
Description
The number of times a permutation switches from increasing to decreasing or decreasing to increasing.
This is the same as the number of inner peaks plus the number of inner valleys and called alternating runs in [2]
Matching statistic: St001330
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 32% ●values known / values provided: 32%●distinct values known / distinct values provided: 88%
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 32% ●values known / values provided: 32%●distinct values known / distinct values provided: 88%
Values
[1,3,2] => 10 => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
[2,1,3] => 01 => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
[1,2,4,3] => 110 => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[1,3,2,4] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
[1,3,4,2] => 100 => [1,2] => ([(1,2)],3)
=> 2 = 3 - 1
[1,4,2,3] => 100 => [1,2] => ([(1,2)],3)
=> 2 = 3 - 1
[1,4,3,2] => 100 => [1,2] => ([(1,2)],3)
=> 2 = 3 - 1
[2,1,3,4] => 011 => [1,2] => ([(1,2)],3)
=> 2 = 3 - 1
[2,1,4,3] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
[2,3,1,4] => 001 => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[3,1,2,4] => 001 => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[3,2,1,4] => 001 => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
[1,2,3,5,4] => 1110 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,2,4,3,5] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
[1,2,4,5,3] => 1100 => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,2,5,3,4] => 1100 => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,2,5,4,3] => 1100 => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,3,2,4,5] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
[1,3,2,5,4] => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
[1,3,4,2,5] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
[1,3,4,5,2] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,3,5,2,4] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,3,5,4,2] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,4,2,3,5] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
[1,4,2,5,3] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,4,3,2,5] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
[1,4,3,5,2] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,4,5,2,3] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,4,5,3,2] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,5,2,3,4] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,5,2,4,3] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,5,3,2,4] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,5,3,4,2] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,5,4,2,3] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[1,5,4,3,2] => 1000 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[2,1,3,4,5] => 0111 => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
[2,1,3,5,4] => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
[2,1,4,3,5] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
[2,1,4,5,3] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
[2,1,5,3,4] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
[2,1,5,4,3] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
[2,3,1,4,5] => 0011 => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,3,1,5,4] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
[2,3,4,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,4,1,3,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[2,4,3,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,1,2,4,5] => 0011 => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,1,2,5,4] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
[3,1,4,2,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,2,1,4,5] => 0011 => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,2,1,5,4] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
[3,2,4,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,4,1,2,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[3,4,2,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[4,1,2,3,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[4,1,3,2,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[4,2,1,3,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[4,2,3,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
[1,2,3,5,4,6] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,2,4,3,5,6] => 11011 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,2,4,3,6,5] => 11010 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[1,2,4,5,3,6] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,2,5,3,4,6] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,2,5,4,3,6] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,3,2,4,6,5] => 10110 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[1,3,4,2,5,6] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,3,4,2,6,5] => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[1,3,4,5,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,3,5,2,4,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,3,5,4,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,4,2,3,5,6] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,4,2,3,6,5] => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[1,4,2,5,3,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,4,3,2,5,6] => 10011 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,4,3,2,6,5] => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[1,4,3,5,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,4,5,2,3,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,4,5,3,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,5,2,3,4,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,5,2,4,3,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,5,3,2,4,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,5,3,4,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,5,4,2,3,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[1,5,4,3,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,1,3,4,6,5] => 01110 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,1,3,5,4,6] => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[2,1,3,5,6,4] => 01100 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,1,3,6,4,5] => 01100 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,1,3,6,5,4] => 01100 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,1,4,5,3,6] => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[2,1,5,3,4,6] => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[2,1,5,4,3,6] => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[2,3,1,4,6,5] => 00110 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,3,1,5,4,6] => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 - 1
[2,3,1,5,6,4] => 00100 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,3,1,6,4,5] => 00100 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,3,1,6,5,4] => 00100 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,3,4,1,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,4,1,3,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
[2,4,3,1,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
Description
The hat guessing number of a graph.
Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of $q$ possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number $HG(G)$ of a graph $G$ is the largest integer $q$ such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of $q$ possible colors.
Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St000456
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 12%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St000456: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 12%
Values
[1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,1,3] => [3,1,2] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,2,4,3] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 3 - 2
[1,3,2,4] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 4 - 2
[1,3,4,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,2,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[2,1,3,4] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 3 - 2
[2,1,4,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([],1)
=> ? = 4 - 2
[2,3,1,4] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,1,2,4] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,1,4] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,2,3,5,4] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,2,4,3,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[1,2,4,5,3] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,2,5,3,4] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,2,5,4,3] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,3,2,4,5] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[1,3,2,5,4] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 5 - 2
[1,3,4,2,5] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[1,3,4,5,2] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,5,2,4] => [4,2,5,3,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,3,5,4,2] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,2,3,5] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[1,4,2,5,3] => [3,5,2,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,4,3,2,5] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[1,4,3,5,2] => [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,5,2,3] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,5,3,2] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,5,2,3,4] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,2,4,3] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,3,2,4] => [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,3,4,2] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,5,4,2,3] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 3 - 2
[2,1,3,4,5] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[2,1,3,5,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[2,1,4,3,5] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 5 - 2
[2,1,4,5,3] => [3,5,4,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[2,1,5,3,4] => [4,3,5,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[2,3,1,4,5] => [5,4,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[2,3,1,5,4] => [4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[2,3,4,1,5] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,4,1,3,5] => [5,3,1,4,2] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[2,4,3,1,5] => [5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,1,2,4,5] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[3,1,2,5,4] => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[3,1,4,2,5] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[3,2,1,4,5] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[3,2,1,5,4] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[3,2,4,1,5] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,4,1,2,5] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,4,2,1,5] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[4,1,2,3,5] => [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[4,1,3,2,5] => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[4,2,1,3,5] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[4,2,3,1,5] => [5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[4,3,1,2,5] => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[4,3,2,1,5] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 3 - 2
[1,2,3,4,6,5] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,3,5,4,6] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 2
[1,2,3,5,6,4] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,3,6,4,5] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,3,6,5,4] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,4,3,5,6] => [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 2
[1,2,4,3,6,5] => [5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 5 - 2
[1,2,4,5,3,6] => [6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 2
[1,2,4,5,6,3] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,4,6,3,5] => [5,3,6,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,4,6,5,3] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,5,3,4,6] => [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 2
[1,2,5,3,6,4] => [4,6,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,5,4,3,6] => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 2
[1,2,5,4,6,3] => [3,6,4,5,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,5,6,3,4] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,5,6,4,3] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,6,3,4,5] => [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,6,3,5,4] => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,6,4,3,5] => [5,3,4,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,3,4,5,6,2] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,4,6,5,2] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,5,4,6,2] => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,5,6,4,2] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,6,4,5,2] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,6,5,4,2] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,3,5,6,2] => [2,6,5,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,3,6,5,2] => [2,5,6,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,5,3,6,2] => [2,6,3,5,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,5,6,2,3] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,5,6,3,2] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,4,6,3,5,2] => [2,5,3,6,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,6,5,2,3] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,6,5,3,2] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,5,3,4,6,2] => [2,6,4,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,3,6,4,2] => [2,4,6,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,4,3,6,2] => [2,6,3,4,5,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,4,6,2,3] => [3,2,6,4,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,4,6,3,2] => [2,3,6,4,5,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,5,6,2,3,4] => [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
Description
The monochromatic index of a connected graph.
This is the maximal number of colours such that there is a colouring of the edges where any two vertices can be joined by a monochromatic path.
For example, a circle graph other than the triangle can be coloured with at most two colours: one edge blue, all the others red.
Matching statistic: St001592
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St001592: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 12%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St001592: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 12%
Values
[1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,1,3] => [3,1,2] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,2,4,3] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 3 - 2
[1,3,2,4] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 4 - 2
[1,3,4,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,2,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[2,1,3,4] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 3 - 2
[2,1,4,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([],1)
=> ? = 4 - 2
[2,3,1,4] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,1,2,4] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,2,1,4] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,2,3,5,4] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,2,4,3,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[1,2,4,5,3] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,2,5,3,4] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,2,5,4,3] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,3,2,4,5] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[1,3,2,5,4] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 5 - 2
[1,3,4,2,5] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[1,3,4,5,2] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,5,2,4] => [4,2,5,3,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,3,5,4,2] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,2,3,5] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[1,4,2,5,3] => [3,5,2,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[1,4,3,2,5] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[1,4,3,5,2] => [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,5,2,3] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,5,3,2] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,5,2,3,4] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,2,4,3] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,3,2,4] => [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,3,4,2] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,5,4,2,3] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 3 - 2
[2,1,3,4,5] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[2,1,3,5,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 2
[2,1,4,3,5] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 5 - 2
[2,1,4,5,3] => [3,5,4,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[2,1,5,3,4] => [4,3,5,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[2,3,1,4,5] => [5,4,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[2,3,1,5,4] => [4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[2,3,4,1,5] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[2,4,1,3,5] => [5,3,1,4,2] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[2,4,3,1,5] => [5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,1,2,4,5] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[3,1,2,5,4] => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[3,1,4,2,5] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[3,2,1,4,5] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 2
[3,2,1,5,4] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 2
[3,2,4,1,5] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,4,1,2,5] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[3,4,2,1,5] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[4,1,2,3,5] => [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[4,1,3,2,5] => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[4,2,1,3,5] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[4,2,3,1,5] => [5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[4,3,1,2,5] => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[4,3,2,1,5] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 1 = 3 - 2
[1,2,3,4,6,5] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,3,5,4,6] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 2
[1,2,3,5,6,4] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,3,6,4,5] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,3,6,5,4] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,4,3,5,6] => [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 2
[1,2,4,3,6,5] => [5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 5 - 2
[1,2,4,5,3,6] => [6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 2
[1,2,4,5,6,3] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,4,6,3,5] => [5,3,6,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,4,6,5,3] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,5,3,4,6] => [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 2
[1,2,5,3,6,4] => [4,6,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,5,4,3,6] => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 2
[1,2,5,4,6,3] => [3,6,4,5,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,5,6,3,4] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,5,6,4,3] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,6,3,4,5] => [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,6,3,5,4] => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,2,6,4,3,5] => [5,3,4,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 2
[1,3,4,5,6,2] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,4,6,5,2] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,5,4,6,2] => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,5,6,4,2] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,6,4,5,2] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,3,6,5,4,2] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,3,5,6,2] => [2,6,5,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,3,6,5,2] => [2,5,6,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,5,3,6,2] => [2,6,3,5,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,5,6,2,3] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,5,6,3,2] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,4,6,3,5,2] => [2,5,3,6,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,6,5,2,3] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,4,6,5,3,2] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,5,3,4,6,2] => [2,6,4,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,3,6,4,2] => [2,4,6,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,4,3,6,2] => [2,6,3,4,5,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,4,6,2,3] => [3,2,6,4,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
[1,5,4,6,3,2] => [2,3,6,4,5,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 1 = 3 - 2
[1,5,6,2,3,4] => [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 1 = 3 - 2
Description
The maximal number of simple paths between any two different vertices of a graph.
Matching statistic: St000379
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St000379: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 12%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St000379: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 12%
Values
[1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,1,3] => [3,1,2] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,2,4,3] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 3 - 3
[1,3,2,4] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 4 - 3
[1,3,4,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,2,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[2,1,3,4] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 3 - 3
[2,1,4,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([],1)
=> ? = 4 - 3
[2,3,1,4] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,1,2,4] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,4] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,2,3,5,4] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,2,4,3,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[1,2,4,5,3] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,2,5,3,4] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,2,5,4,3] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,3,2,4,5] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[1,3,2,5,4] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 5 - 3
[1,3,4,2,5] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[1,3,4,5,2] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,5,2,4] => [4,2,5,3,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,3,5,4,2] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,2,3,5] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[1,4,2,5,3] => [3,5,2,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,4,3,2,5] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[1,4,3,5,2] => [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,5,2,3] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,5,3,2] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,5,2,3,4] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,2,4,3] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,3,2,4] => [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,3,4,2] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,5,4,2,3] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 3 - 3
[2,1,3,4,5] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[2,1,3,5,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[2,1,4,3,5] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 5 - 3
[2,1,4,5,3] => [3,5,4,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[2,1,5,3,4] => [4,3,5,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[2,3,1,4,5] => [5,4,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[2,3,1,5,4] => [4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[2,3,4,1,5] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,1,3,5] => [5,3,1,4,2] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[2,4,3,1,5] => [5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,1,2,4,5] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[3,1,2,5,4] => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[3,1,4,2,5] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[3,2,1,4,5] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[3,2,1,5,4] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[3,2,4,1,5] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,4,1,2,5] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,4,2,1,5] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[4,1,2,3,5] => [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[4,1,3,2,5] => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[4,2,1,3,5] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[4,2,3,1,5] => [5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[4,3,1,2,5] => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[4,3,2,1,5] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 3 - 3
[1,2,3,4,6,5] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,3,5,4,6] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 3
[1,2,3,5,6,4] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,3,6,4,5] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,3,6,5,4] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,4,3,5,6] => [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 3
[1,2,4,3,6,5] => [5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 5 - 3
[1,2,4,5,3,6] => [6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 3
[1,2,4,5,6,3] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,4,6,3,5] => [5,3,6,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,4,6,5,3] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,5,3,4,6] => [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 3
[1,2,5,3,6,4] => [4,6,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,5,4,3,6] => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 3
[1,2,5,4,6,3] => [3,6,4,5,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,5,6,3,4] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,5,6,4,3] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,6,3,4,5] => [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,6,3,5,4] => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,6,4,3,5] => [5,3,4,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,3,4,5,6,2] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,4,6,5,2] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,5,4,6,2] => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,5,6,4,2] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,6,4,5,2] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,6,5,4,2] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,5,6,2] => [2,6,5,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,6,5,2] => [2,5,6,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,5,3,6,2] => [2,6,3,5,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,5,6,2,3] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,5,6,3,2] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,4,6,3,5,2] => [2,5,3,6,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,6,5,2,3] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,6,5,3,2] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,5,3,4,6,2] => [2,6,4,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,3,6,4,2] => [2,4,6,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,4,3,6,2] => [2,6,3,4,5,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,4,6,2,3] => [3,2,6,4,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,4,6,3,2] => [2,3,6,4,5,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,5,6,2,3,4] => [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
Description
The number of Hamiltonian cycles in a graph.
A Hamiltonian cycle in a graph $G$ is a subgraph (this is, a subset of the edges) that is a cycle which contains every vertex of $G$.
Since it is unclear whether the graph on one vertex is Hamiltonian, the statistic is undefined for this graph.
Matching statistic: St000455
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 12%
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00274: Graphs —block-cut tree⟶ Graphs
St000455: Graphs ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 12%
Values
[1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,1,3] => [3,1,2] => ([(0,2),(1,2)],3)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,2,4,3] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 3 - 3
[1,3,2,4] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 4 - 3
[1,3,4,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,2,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[2,1,3,4] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 3 - 3
[2,1,4,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([],1)
=> ? = 4 - 3
[2,3,1,4] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,1,2,4] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,2,1,4] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,2,3,5,4] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,2,4,3,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[1,2,4,5,3] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,2,5,3,4] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,2,5,4,3] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,3,2,4,5] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[1,3,2,5,4] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 5 - 3
[1,3,4,2,5] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[1,3,4,5,2] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,5,2,4] => [4,2,5,3,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,3,5,4,2] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,2,3,5] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[1,4,2,5,3] => [3,5,2,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[1,4,3,2,5] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[1,4,3,5,2] => [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,5,2,3] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,5,3,2] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,5,2,3,4] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,2,4,3] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,3,2,4] => [4,2,3,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,3,4,2] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,5,4,2,3] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,5,4,3,2] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 3 - 3
[2,1,3,4,5] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[2,1,3,5,4] => [4,5,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 4 - 3
[2,1,4,3,5] => [5,3,4,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 5 - 3
[2,1,4,5,3] => [3,5,4,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[2,1,5,3,4] => [4,3,5,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[2,1,5,4,3] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[2,3,1,4,5] => [5,4,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[2,3,1,5,4] => [4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[2,3,4,1,5] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[2,4,1,3,5] => [5,3,1,4,2] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[2,4,3,1,5] => [5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,1,2,4,5] => [5,4,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[3,1,2,5,4] => [4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[3,1,4,2,5] => [5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[3,2,1,4,5] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 3 - 3
[3,2,1,5,4] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 4 - 3
[3,2,4,1,5] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,4,1,2,5] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[3,4,2,1,5] => [5,1,2,4,3] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[4,1,2,3,5] => [5,3,2,1,4] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[4,1,3,2,5] => [5,2,3,1,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[4,2,1,3,5] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[4,2,3,1,5] => [5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[4,3,1,2,5] => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[4,3,2,1,5] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 3 - 3
[1,2,3,4,6,5] => [5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,3,5,4,6] => [6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 3
[1,2,3,5,6,4] => [4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,3,6,4,5] => [5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,3,6,5,4] => [4,5,6,3,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,4,3,5,6] => [6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 3
[1,2,4,3,6,5] => [5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 5 - 3
[1,2,4,5,3,6] => [6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 3
[1,2,4,5,6,3] => [3,6,5,4,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,4,6,3,5] => [5,3,6,4,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,4,6,5,3] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,5,3,4,6] => [6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 3
[1,2,5,3,6,4] => [4,6,3,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,5,4,3,6] => [6,3,4,5,2,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 4 - 3
[1,2,5,4,6,3] => [3,6,4,5,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,5,6,3,4] => [4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,5,6,4,3] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,6,3,4,5] => [5,4,3,6,2,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,6,3,5,4] => [4,5,3,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,2,6,4,3,5] => [5,3,4,6,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([],1)
=> ? = 3 - 3
[1,3,4,5,6,2] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,4,6,5,2] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,5,4,6,2] => [2,6,4,5,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,5,6,4,2] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,6,4,5,2] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,3,6,5,4,2] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,5,6,2] => [2,6,5,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,3,6,5,2] => [2,5,6,3,4,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,5,3,6,2] => [2,6,3,5,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,5,6,2,3] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,5,6,3,2] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,4,6,3,5,2] => [2,5,3,6,4,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,6,5,2,3] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,4,6,5,3,2] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,5,3,4,6,2] => [2,6,4,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,3,6,4,2] => [2,4,6,3,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,4,3,6,2] => [2,6,3,4,5,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,4,6,2,3] => [3,2,6,4,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
[1,5,4,6,3,2] => [2,3,6,4,5,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,3),(1,3),(2,3)],4)
=> 0 = 3 - 3
[1,5,6,2,3,4] => [4,3,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,2),(1,2)],3)
=> 0 = 3 - 3
Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
Matching statistic: St001388
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
St001388: Permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
St001388: Permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 50%
Values
[1,3,2] => [1,3,2] => [1,3,2] => [3,1,2] => 1 = 3 - 2
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 1 = 3 - 2
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [4,1,2,3] => 1 = 3 - 2
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [3,1,2,4] => 2 = 4 - 2
[1,3,4,2] => [1,4,3,2] => [1,4,3,2] => [4,3,1,2] => 1 = 3 - 2
[1,4,2,3] => [1,4,3,2] => [1,4,3,2] => [4,3,1,2] => 1 = 3 - 2
[1,4,3,2] => [1,4,3,2] => [1,4,3,2] => [4,3,1,2] => 1 = 3 - 2
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1 = 3 - 2
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [4,2,1,3] => 2 = 4 - 2
[2,3,1,4] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 1 = 3 - 2
[3,1,2,4] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 1 = 3 - 2
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 1 = 3 - 2
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => 1 = 3 - 2
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [4,1,2,3,5] => 2 = 4 - 2
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 1 = 3 - 2
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 1 = 3 - 2
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => 1 = 3 - 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [3,1,2,4,5] => 2 = 4 - 2
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [5,3,1,2,4] => 3 = 5 - 2
[1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => [4,3,1,2,5] => 2 = 4 - 2
[1,3,4,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,3,5,2,4] => [1,4,5,2,3] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,3,5,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,4,2,3,5] => [1,4,3,2,5] => [1,4,3,2,5] => [4,3,1,2,5] => 2 = 4 - 2
[1,4,2,5,3] => [1,5,3,4,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => [4,3,1,2,5] => 2 = 4 - 2
[1,4,3,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,4,5,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,5,2,3,4] => [1,5,3,4,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,5,2,4,3] => [1,5,3,4,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,5,3,2,4] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,5,4,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => [5,4,3,1,2] => 1 = 3 - 2
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1 = 3 - 2
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [5,2,1,3,4] => 2 = 4 - 2
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => [4,2,1,3,5] => 3 = 5 - 2
[2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3] => [5,4,2,1,3] => 2 = 4 - 2
[2,1,5,3,4] => [2,1,5,4,3] => [2,1,5,4,3] => [5,4,2,1,3] => 2 = 4 - 2
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => [5,4,2,1,3] => 2 = 4 - 2
[2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 1 = 3 - 2
[2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [5,3,2,1,4] => 2 = 4 - 2
[2,3,4,1,5] => [4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1 = 3 - 2
[2,4,1,3,5] => [3,4,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1 = 3 - 2
[2,4,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1 = 3 - 2
[3,1,2,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 1 = 3 - 2
[3,1,2,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [5,3,2,1,4] => 2 = 4 - 2
[3,1,4,2,5] => [4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 1 = 3 - 2
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => 1 = 3 - 2
[1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => ? = 3 - 2
[1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => ? = 4 - 2
[1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => ? = 3 - 2
[1,2,3,4,7,5,6] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => ? = 3 - 2
[1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => ? = 3 - 2
[1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => ? = 4 - 2
[1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [7,5,1,2,3,4,6] => ? = 5 - 2
[1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => ? = 4 - 2
[1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,5,7,4,6] => [1,2,3,6,7,4,5] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,5,7,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,6,4,5,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => ? = 4 - 2
[1,2,3,6,4,7,5] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => ? = 4 - 2
[1,2,3,6,5,7,4] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,6,7,4,5] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,6,7,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,7,4,5,6] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,7,4,6,5] => [1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,7,5,4,6] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,7,5,6,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,7,6,4,5] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 3 - 2
[1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => ? = 4 - 2
[1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [7,4,1,2,3,5,6] => ? = 5 - 2
[1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [6,4,1,2,3,5,7] => ? = 6 - 2
[1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [7,6,4,1,2,3,5] => ? = 5 - 2
[1,2,4,3,7,5,6] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [7,6,4,1,2,3,5] => ? = 5 - 2
[1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [7,6,4,1,2,3,5] => ? = 5 - 2
[1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ? = 4 - 2
[1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [7,5,4,1,2,3,6] => ? = 4 - 2
[1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => ? = 4 - 2
[1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,5,7,3,6] => [1,2,6,4,7,3,5] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,5,7,6,3] => [1,2,7,4,6,5,3] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,6,3,5,7] => [1,2,5,6,3,4,7] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => ? = 4 - 2
[1,2,4,6,3,7,5] => [1,2,5,7,3,6,4] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,6,5,3,7] => [1,2,6,5,4,3,7] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => ? = 4 - 2
[1,2,4,6,5,7,3] => [1,2,7,5,4,6,3] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,6,7,3,5] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,6,7,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,7,3,5,6] => [1,2,5,7,3,6,4] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,7,3,6,5] => [1,2,5,7,3,6,4] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,7,5,3,6] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,7,5,6,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,7,6,3,5] => [1,2,6,7,5,3,4] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,4,7,6,5,3] => [1,2,7,6,5,4,3] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => ? = 3 - 2
[1,2,5,3,4,6,7] => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => ? = 4 - 2
[1,2,5,3,4,7,6] => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [7,5,4,1,2,3,6] => ? = 4 - 2
[1,2,5,3,6,4,7] => [1,2,6,4,5,3,7] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => ? = 4 - 2
Description
The number of non-attacking neighbors of a permutation.
For a permutation $\sigma$, the indices $i$ and $i+1$ are attacking if $|\sigma(i)-\sigma(i+1)| = 1$.
Visually, this is, for $\sigma$ considered as a placement of kings on a chessboard, if the kings placed in columns $i$ and $i+1$ are non-attacking.
Matching statistic: St001060
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001060: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Values
[1,3,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
=> ? = 3
[2,1,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
=> ? = 3
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
=> ? = 3
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
=> ? = 4
[1,3,4,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,4,2,3] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,4,3,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> 3
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => ([(2,3)],4)
=> ? = 3
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? = 4
[2,3,1,4] => [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[3,1,2,4] => [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ([(3,4)],5)
=> ? = 3
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => ([(3,4)],5)
=> ? = 4
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 3
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 3
[1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 3
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => ([(3,4)],5)
=> ? = 4
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
=> ? = 5
[1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ? = 4
[1,3,4,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,3,5,2,4] => [1,4,5,2,3] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,3,5,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,4,2,3,5] => [1,4,3,2,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ? = 4
[1,4,2,5,3] => [1,5,3,4,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
=> ? = 4
[1,4,3,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,4,5,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,5,2,3,4] => [1,5,3,4,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,5,2,4,3] => [1,5,3,4,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,5,3,2,4] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,5,4,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ([(3,4)],5)
=> ? = 3
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ([(1,4),(2,3)],5)
=> ? = 4
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ([(1,4),(2,3)],5)
=> ? = 5
[2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4
[2,1,5,3,4] => [2,1,5,4,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4
[2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ? = 3
[2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4
[2,3,4,1,5] => [4,2,3,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,4,1,3,5] => [3,4,1,2,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[2,4,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,1,2,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ? = 3
[3,1,2,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4
[3,1,4,2,5] => [4,2,3,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> ? = 3
[3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4
[3,2,4,1,5] => [4,2,3,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,4,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[3,4,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[4,1,2,3,5] => [4,2,3,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[4,1,3,2,5] => [4,2,3,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[4,2,1,3,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[4,2,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[4,3,1,2,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3
[1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => ([(4,5)],6)
=> ? = 3
[1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => ([(4,5)],6)
=> ? = 4
[1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,3,6,4,5] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,3,6,5,4] => [1,2,3,6,5,4] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => ([(4,5)],6)
=> ? = 4
[1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6)
=> ? = 5
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6)
=> ? = 4
[1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,4,6,3,5] => [1,2,5,6,3,4] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,4,6,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,5,3,4,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6)
=> ? = 4
[1,2,5,3,6,4] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,5,4,3,6] => [1,2,5,4,3,6] => [1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6)
=> ? = 4
[1,2,5,4,6,3] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,5,6,3,4] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,5,6,4,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,6,3,4,5] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,6,3,5,4] => [1,2,6,4,5,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,6,4,3,5] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,6,4,5,3] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,2,6,5,3,4] => [1,2,6,5,4,3] => [1,2,6,5,4,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 3
[1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,5,2,6,4] => [1,4,6,2,5,3] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,5,4,6,2] => [1,6,4,3,5,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,6,2,4,5] => [1,4,6,2,5,3] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,6,2,5,4] => [1,4,6,2,5,3] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,6,4,2,5] => [1,5,6,4,2,3] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,6,4,5,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,6,5,2,4] => [1,5,6,4,2,3] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,3,6,5,4,2] => [1,6,5,4,3,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,2,5,6,3] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,2,6,3,5] => [1,5,3,6,2,4] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,2,6,5,3] => [1,6,3,5,4,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,3,5,6,2] => [1,6,3,4,5,2] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
[1,4,3,6,2,5] => [1,5,3,6,2,4] => [1,6,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3
Description
The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
Matching statistic: St001645
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 12%
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001645: Graphs ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 12%
Values
[1,3,2] => [1,3,2] => [1,3,2] => ([(1,2)],3)
=> ? = 3 + 4
[2,1,3] => [2,1,3] => [2,1,3] => ([(1,2)],3)
=> ? = 3 + 4
[1,2,4,3] => [1,2,4,3] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 3 + 4
[1,3,2,4] => [1,3,2,4] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 4 + 4
[1,3,4,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 3 + 4
[1,4,2,3] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 3 + 4
[1,4,3,2] => [1,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 3 + 4
[2,1,3,4] => [2,1,3,4] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? = 3 + 4
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
=> ? = 4 + 4
[2,3,1,4] => [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? = 3 + 4
[3,1,2,4] => [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? = 3 + 4
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> ? = 3 + 4
[1,2,3,5,4] => [1,2,3,5,4] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,2,4,3,5] => [1,2,4,3,5] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,2,4,5,3] => [1,2,5,4,3] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,2,5,3,4] => [1,2,5,4,3] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,2,5,4,3] => [1,2,5,4,3] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,3,2,4,5] => [1,3,2,4,5] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,3,2,5,4] => [1,3,2,5,4] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 5 + 4
[1,3,4,2,5] => [1,4,3,2,5] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,3,4,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,3,5,2,4] => [1,4,5,2,3] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,3,5,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,4,2,3,5] => [1,4,3,2,5] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,4,2,5,3] => [1,5,3,4,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,4,3,2,5] => [1,4,3,2,5] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[1,4,3,5,2] => [1,5,3,4,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,4,5,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,4,5,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,5,2,3,4] => [1,5,3,4,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,5,2,4,3] => [1,5,3,4,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,5,3,2,4] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,5,3,4,2] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,5,4,2,3] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 5 + 4
[2,1,4,5,3] => [2,1,5,4,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[2,1,5,3,4] => [2,1,5,4,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[2,3,1,4,5] => [3,2,1,4,5] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[2,3,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[2,3,4,1,5] => [4,2,3,1,5] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[2,4,1,3,5] => [3,4,1,2,5] => [3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[2,4,3,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[3,1,2,4,5] => [3,2,1,4,5] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[3,1,2,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 4 + 4
[3,1,4,2,5] => [4,2,3,1,5] => [4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,5,4] => ([(0,1),(2,3),(2,4),(3,4)],5)
=> ? = 3 + 4
[2,4,5,6,1,3,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,4,5,6,3,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,4,6,1,3,5,7] => [4,5,6,1,2,3,7] => [4,7,6,1,5,3,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,4,6,1,5,3,7] => [4,6,5,1,3,2,7] => [4,7,6,1,5,3,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,4,6,3,5,1,7] => [6,4,5,2,3,1,7] => [6,4,7,2,5,1,3] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,5,3,6,1,4,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,5,3,6,4,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,5,4,6,1,3,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,5,4,6,3,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,5,6,1,3,4,7] => [4,6,5,1,3,2,7] => [4,7,6,1,5,3,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,5,6,1,4,3,7] => [4,6,5,1,3,2,7] => [4,7,6,1,5,3,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,6,3,4,1,5,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,6,3,4,5,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,6,3,5,1,4,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,6,3,5,4,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,6,4,1,3,5,7] => [4,6,5,1,3,2,7] => [4,7,6,1,5,3,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,6,4,1,5,3,7] => [4,6,5,1,3,2,7] => [4,7,6,1,5,3,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,6,5,1,3,4,7] => [4,6,5,1,3,2,7] => [4,7,6,1,5,3,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[2,6,5,1,4,3,7] => [4,6,5,1,3,2,7] => [4,7,6,1,5,3,2] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,4,5,6,1,2,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,4,5,6,2,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,4,6,1,5,2,7] => [6,4,5,2,3,1,7] => [6,4,7,2,5,1,3] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,4,6,2,5,1,7] => [6,4,5,2,3,1,7] => [6,4,7,2,5,1,3] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,5,1,6,2,4,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,5,1,6,4,2,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,5,2,6,1,4,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,5,2,6,4,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,5,4,6,1,2,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,5,4,6,2,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,6,1,4,2,5,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,6,1,4,5,2,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,6,1,5,2,4,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,6,1,5,4,2,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,6,2,4,1,5,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,6,2,4,5,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,6,2,5,1,4,7] => [5,6,3,4,1,2,7] => [5,7,3,6,1,4,2] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[3,6,2,5,4,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,2,5,6,1,3,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,2,5,6,3,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,2,6,1,5,3,7] => [6,4,5,2,3,1,7] => [6,4,7,2,5,1,3] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,2,6,3,5,1,7] => [6,4,5,2,3,1,7] => [6,4,7,2,5,1,3] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,3,5,6,1,2,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,3,5,6,2,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,3,6,1,5,2,7] => [6,4,5,2,3,1,7] => [6,4,7,2,5,1,3] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,3,6,2,5,1,7] => [6,4,5,2,3,1,7] => [6,4,7,2,5,1,3] => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,5,1,6,2,3,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,5,1,6,3,2,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,5,2,6,1,3,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,5,2,6,3,1,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
[4,5,3,6,1,2,7] => [6,5,3,4,2,1,7] => [6,5,3,7,2,1,4] => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> 7 = 3 + 4
Description
The pebbling number of a connected graph.
The following 11 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001964The interval resolution global dimension of a poset. St000741The Colin de Verdière graph invariant. St001488The number of corners of a skew partition. St001537The number of cyclic crossings of a permutation. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001876The number of 2-regular simple modules in the incidence algebra of the lattice. St000454The largest eigenvalue of a graph if it is integral. St000422The energy of a graph, if it is integral. St000181The number of connected components of the Hasse diagram for the poset. St001890The maximum magnitude of the Möbius function of a poset.
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!