searching the database
Your data matches 2 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
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
Mp00133: Integer compositions —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%
Mp00133: Integer compositions —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
([(1,2)],3)
=> [1,2] => [1,1] => [2] => 3
([(0,1),(0,2),(1,2)],3)
=> [2,1] => [1,1] => [2] => 3
([(2,3)],4)
=> [1,3] => [1,1] => [2] => 3
([(1,3),(2,3)],4)
=> [1,1,2] => [2,1] => [1,1] => 3
([(0,3),(1,3),(2,3)],4)
=> [1,2,1] => [1,1,1] => [3] => 4
([(0,2),(0,3),(1,2),(1,3)],4)
=> [1,2,1] => [1,1,1] => [3] => 4
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [2,1,1] => [1,2] => [1,1] => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [3,1] => [1,1] => [2] => 3
([(3,4)],5)
=> [1,4] => [1,1] => [2] => 3
([(2,4),(3,4)],5)
=> [1,1,3] => [2,1] => [1,1] => 3
([(1,4),(2,4),(3,4)],5)
=> [1,2,2] => [1,2] => [1,1] => 3
([(0,4),(1,4),(2,4),(3,4)],5)
=> [1,3,1] => [1,1,1] => [3] => 4
([(1,4),(2,3)],5)
=> [2,3] => [1,1] => [2] => 3
([(1,4),(2,3),(3,4)],5)
=> [1,1,1,2] => [3,1] => [1,1] => 3
([(0,1),(2,4),(3,4)],5)
=> [1,1,1,2] => [3,1] => [1,1] => 3
([(2,3),(2,4),(3,4)],5)
=> [2,3] => [1,1] => [2] => 3
([(1,4),(2,3),(2,4),(3,4)],5)
=> [1,1,1,2] => [3,1] => [1,1] => 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [1,1,2,1] => [2,1,1] => [1,2] => 4
([(1,3),(1,4),(2,3),(2,4)],5)
=> [1,2,2] => [1,2] => [1,1] => 3
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,1,2] => [1,1,1] => [3] => 4
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [1,1,2,1] => [2,1,1] => [1,2] => 4
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => [1,1] => 3
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,1,2] => [1,1,1] => [3] => 4
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [1,2,1,1] => [1,1,2] => [2,1] => 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [2,1] => [1,1] => 3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2] => [1,1] => [2] => 3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [1,2,1,1] => [1,1,2] => [2,1] => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,1,1,1] => [1,3] => [1,1] => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => [1,1] => 3
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,1,1] => [1,2] => [1,1] => 3
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1] => [1,1] => [2] => 3
([(4,5)],6)
=> [1,5] => [1,1] => [2] => 3
([(3,5),(4,5)],6)
=> [1,1,4] => [2,1] => [1,1] => 3
([(2,5),(3,5),(4,5)],6)
=> [1,2,3] => [1,1,1] => [3] => 4
([(1,5),(2,5),(3,5),(4,5)],6)
=> [1,3,2] => [1,1,1] => [3] => 4
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [1,4,1] => [1,1,1] => [3] => 4
([(2,5),(3,4)],6)
=> [2,4] => [1,1] => [2] => 3
([(2,5),(3,4),(4,5)],6)
=> [1,1,1,3] => [3,1] => [1,1] => 3
([(1,2),(3,5),(4,5)],6)
=> [1,1,1,3] => [3,1] => [1,1] => 3
([(3,4),(3,5),(4,5)],6)
=> [2,4] => [1,1] => [2] => 3
([(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,1,1,2] => [4,1] => [1,1] => 3
([(0,1),(2,5),(3,5),(4,5)],6)
=> [1,1,2,2] => [2,2] => [2] => 3
([(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,3] => [3,1] => [1,1] => 3
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,2,1,1] => [2,1,2] => [1,1,1] => 4
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,2,2] => [2,2] => [2] => 3
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,3,1] => [2,1,1] => [1,2] => 4
([(2,4),(2,5),(3,4),(3,5)],6)
=> [1,2,3] => [1,1,1] => [3] => 4
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [1,1,1,1,2] => [4,1] => [1,1] => 3
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,1,3] => [1,1,1] => [3] => 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,2] => [4,1] => [1,1] => 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: St001330
Mp00152: Graphs —Laplacian multiplicities⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 80%
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 48% ●values known / values provided: 48%●distinct values known / distinct values provided: 80%
Values
([(1,2)],3)
=> [1,2] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(0,1),(0,2),(1,2)],3)
=> [2,1] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(2,3)],4)
=> [1,3] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(1,3),(2,3)],4)
=> [1,1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
([(0,3),(1,3),(2,3)],4)
=> [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(0,2),(0,3),(1,2),(1,3)],4)
=> [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [2,1,1] => [1,2] => ([(1,2)],3)
=> 2 = 3 - 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> [3,1] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(3,4)],5)
=> [1,4] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(2,4),(3,4)],5)
=> [1,1,3] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
([(1,4),(2,4),(3,4)],5)
=> [1,2,2] => [1,2] => ([(1,2)],3)
=> 2 = 3 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(1,4),(2,3)],5)
=> [2,3] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(1,4),(2,3),(3,4)],5)
=> [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,1),(2,4),(3,4)],5)
=> [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(2,3),(2,4),(3,4)],5)
=> [2,3] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(1,4),(2,3),(2,4),(3,4)],5)
=> [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
=> [1,2,2] => [1,2] => ([(1,2)],3)
=> 2 = 3 - 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
([(0,1),(2,3),(2,4),(3,4)],5)
=> [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,2] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 4 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [2,1,1,1] => [1,3] => ([(2,3)],4)
=> 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
=> [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [3,1,1] => [1,2] => ([(1,2)],3)
=> 2 = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> [4,1] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(4,5)],6)
=> [1,5] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(3,5),(4,5)],6)
=> [1,1,4] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 3 - 1
([(2,5),(3,5),(4,5)],6)
=> [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
=> [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(2,5),(3,4)],6)
=> [2,4] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(2,5),(3,4),(4,5)],6)
=> [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(1,2),(3,5),(4,5)],6)
=> [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(3,4),(3,5),(4,5)],6)
=> [2,4] => [1,1] => ([(0,1)],2)
=> 2 = 3 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 3 - 1
([(0,1),(2,5),(3,5),(4,5)],6)
=> [1,1,2,2] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 3 - 1
([(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,2,2] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(2,4),(2,5),(3,4),(3,5)],6)
=> [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 3 - 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 3 - 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 3 - 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,1,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,2,2] => [2,2] => ([(1,3),(2,3)],4)
=> 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 4 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
=> [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 3 - 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [2,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
=> [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(1,2),(3,6),(4,6),(5,6)],7)
=> [1,1,2,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> [1,1,2,1,2] => [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
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> [1,1,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [1,1,2,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> [1,1,3,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [1,1,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
=> [1,1,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
=> [1,1,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [1,1,2,1,2] => [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
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> [1,1,1,2,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
=> [1,1,3,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [1,1,1,2,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> [1,1,1,2,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [1,1,1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [1,1,2,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> [1,1,1,2,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [1,1,2,1,2] => [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
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
=> [1,1,1,2,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [1,1,2,1,1,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [1,1,2,1,2] => [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
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> [1,1,2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 4 - 1
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [1,1,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ? = 4 - 1
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [1,1,2,1,1,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ? = 4 - 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> [1,1,3,1,1] => [2,1,2] => ([(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.
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!