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Your data matches 32 different statistics following compositions of up to 3 maps.
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Matching statistic: St000911
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Values
([],1)
=> 1
([],2)
=> 1
([(0,1)],2)
=> 2
([],3)
=> 1
([(1,2)],3)
=> 2
([(0,1),(0,2)],3)
=> 1
([(0,2),(2,1)],3)
=> 3
([(0,2),(1,2)],3)
=> 1
([],4)
=> 1
([(2,3)],4)
=> 2
([(1,2),(1,3)],4)
=> 1
([(0,1),(0,2),(0,3)],4)
=> 1
([(0,2),(0,3),(3,1)],4)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
([(1,2),(2,3)],4)
=> 3
([(0,3),(3,1),(3,2)],4)
=> 1
([(1,3),(2,3)],4)
=> 1
([(0,3),(1,3),(3,2)],4)
=> 1
([(0,3),(1,3),(2,3)],4)
=> 1
([(0,3),(1,2)],4)
=> 4
([(0,3),(1,2),(1,3)],4)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
([(0,3),(2,1),(3,2)],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> 2
([],5)
=> 1
([(3,4)],5)
=> 2
([(2,3),(2,4)],5)
=> 1
([(1,2),(1,3),(1,4)],5)
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 1
([(1,3),(1,4),(4,2)],5)
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 2
([(2,3),(3,4)],5)
=> 3
([(1,4),(4,2),(4,3)],5)
=> 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> 1
([(2,4),(3,4)],5)
=> 1
([(1,4),(2,4),(4,3)],5)
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> 2
([(1,4),(2,4),(3,4)],5)
=> 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> 1
([(0,4),(1,4),(2,3)],5)
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> 1
Description
The number of maximal antichains of maximal size in a poset.
Matching statistic: St000228
Values
([],1)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([],2)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([],3)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([(0,1),(0,2)],3)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> [3]
=> 3
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([],4)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([(1,2),(1,3)],4)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> [3]
=> 3
([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> [3,1]
=> 4
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> [3]
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> [4]
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> [3,1]
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> [3]
=> 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> [3]
=> 3
([(1,4),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> [2]
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> [1]
=> 1
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ?
=> ?
=> ? = 16
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
=> ([(0,5),(0,6),(1,9),(2,8),(3,10),(4,11),(5,3),(5,13),(6,4),(6,13),(8,7),(9,7),(10,2),(10,12),(11,1),(11,12),(12,8),(12,9),(13,10),(13,11)],14)
=> ?
=> ?
=> ? = 14
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
=> ([(0,3),(0,4),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(7,5),(7,6),(8,9),(8,10),(9,11),(10,11)],12)
=> ?
=> ?
=> ? = 12
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
=> ?
=> ?
=> ? = 10
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
=> ([(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(8,9),(8,10),(9,11),(10,11),(11,3),(11,4)],12)
=> ?
=> ?
=> ? = 12
([(0,7),(1,6),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> [5,3,3,3,1,1]
=> ? = 16
Description
The size of a partition.
This statistic is the constant statistic of the level sets.
Matching statistic: St001616
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 1
([],2)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> 2
([],3)
=> ([],1)
=> 1
([(1,2)],3)
=> ([(0,1)],2)
=> 2
([(0,1),(0,2)],3)
=> ([],1)
=> 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
([(0,2),(1,2)],3)
=> ([],1)
=> 1
([],4)
=> ([],1)
=> 1
([(2,3)],4)
=> ([(0,1)],2)
=> 2
([(1,2),(1,3)],4)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> 1
([(1,3),(2,3)],4)
=> ([],1)
=> 1
([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> 2
([],5)
=> ([],1)
=> 1
([(3,4)],5)
=> ([(0,1)],2)
=> 2
([(2,3),(2,4)],5)
=> ([],1)
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([],1)
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 2
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 3
([(1,4),(4,2),(4,3)],5)
=> ([],1)
=> 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> 1
([(2,4),(3,4)],5)
=> ([],1)
=> 1
([(1,4),(2,4),(4,3)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> 2
([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> 1
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 10
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ? = 10
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ? = 16
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
=> ([(0,5),(0,6),(1,9),(2,8),(3,10),(4,11),(5,3),(5,13),(6,4),(6,13),(8,7),(9,7),(10,2),(10,12),(11,1),(11,12),(12,8),(12,9),(13,10),(13,11)],14)
=> ? = 14
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
=> ([(0,3),(0,4),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(7,5),(7,6),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 12
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 10
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
=> ? = 10
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
=> ([(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(8,9),(8,10),(9,11),(10,11),(11,3),(11,4)],12)
=> ? = 12
([(0,7),(1,6),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 16
Description
The number of neutral elements in a lattice.
An element $e$ of the lattice $L$ is neutral if the sublattice generated by $e$, $x$ and $y$ is distributive for all $x, y \in L$.
Matching statistic: St000479
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(1,2),(1,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(1,4),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ?
=> ?
=> ? = 16
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
=> ([(0,5),(0,6),(1,9),(2,8),(3,10),(4,11),(5,3),(5,13),(6,4),(6,13),(8,7),(9,7),(10,2),(10,12),(11,1),(11,12),(12,8),(12,9),(13,10),(13,11)],14)
=> ?
=> ?
=> ? = 14
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
=> ([(0,3),(0,4),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(7,5),(7,6),(8,9),(8,10),(9,11),(10,11)],12)
=> ?
=> ?
=> ? = 12
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
=> ?
=> ?
=> ? = 10
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
=> ([(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(8,9),(8,10),(9,11),(10,11),(11,3),(11,4)],12)
=> ?
=> ?
=> ? = 12
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,7),(1,6),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(2,5),(2,7),(2,8),(2,9),(2,11),(2,14),(2,15),(3,4),(3,6),(3,7),(3,9),(3,11),(3,13),(3,15),(4,6),(4,7),(4,8),(4,11),(4,12),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(6,7),(6,10),(6,14),(6,15),(7,10),(7,12),(7,13),(8,9),(8,10),(8,13),(8,15),(9,10),(9,12),(9,14),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(11,15),(12,13),(12,14),(12,15),(13,14),(13,15),(14,15)],16)
=> ? = 16
([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(2,5),(3,4),(4,6),(5,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
Description
The Ramsey number of a graph.
This is the smallest integer $n$ such that every two-colouring of the edges of the complete graph $K_n$ contains a (not necessarily induced) monochromatic copy of the given graph. [1]
Thus, the Ramsey number of the complete graph $K_n$ is the ordinary Ramsey number $R(n,n)$. Very few of these numbers are known, in particular, it is only known that $43\leq R(5,5)\leq 48$. [2,3,4,5]
Matching statistic: St000550
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 1
([],2)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> 2
([],3)
=> ([],1)
=> 1
([(1,2)],3)
=> ([(0,1)],2)
=> 2
([(0,1),(0,2)],3)
=> ([],1)
=> 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
([(0,2),(1,2)],3)
=> ([],1)
=> 1
([],4)
=> ([],1)
=> 1
([(2,3)],4)
=> ([(0,1)],2)
=> 2
([(1,2),(1,3)],4)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> 1
([(1,3),(2,3)],4)
=> ([],1)
=> 1
([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> 2
([],5)
=> ([],1)
=> 1
([(3,4)],5)
=> ([(0,1)],2)
=> 2
([(2,3),(2,4)],5)
=> ([],1)
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([],1)
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 2
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 3
([(1,4),(4,2),(4,3)],5)
=> ([],1)
=> 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> 1
([(2,4),(3,4)],5)
=> ([],1)
=> 1
([(1,4),(2,4),(4,3)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> 2
([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 8
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 8
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 8
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 8
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 8
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 8
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ? = 10
([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ? = 8
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ? = 16
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
=> ([(0,5),(0,6),(1,9),(2,8),(3,10),(4,11),(5,3),(5,13),(6,4),(6,13),(8,7),(9,7),(10,2),(10,12),(11,1),(11,12),(12,8),(12,9),(13,10),(13,11)],14)
=> ? = 14
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
=> ([(0,3),(0,4),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(7,5),(7,6),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 12
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ? = 8
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
=> ? = 10
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
=> ([(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(8,9),(8,10),(9,11),(10,11),(11,3),(11,4)],12)
=> ? = 12
([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ? = 8
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 8
([(0,7),(1,6),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 16
([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 9
([(2,5),(3,4),(4,6),(5,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 9
Description
The number of modular elements of a lattice.
A pair $(x, y)$ of elements of a lattice $L$ is a modular pair if for every $z\geq y$ we have that $(y\vee x) \wedge z = y \vee (x \wedge z)$. An element $x$ is left-modular if $(x, y)$ is a modular pair for every $y\in L$, and is modular if both $(x, y)$ and $(y, x)$ are modular pairs for every $y\in L$.
Matching statistic: St000551
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
([],1)
=> ([],1)
=> 1
([],2)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> 2
([],3)
=> ([],1)
=> 1
([(1,2)],3)
=> ([(0,1)],2)
=> 2
([(0,1),(0,2)],3)
=> ([],1)
=> 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 3
([(0,2),(1,2)],3)
=> ([],1)
=> 1
([],4)
=> ([],1)
=> 1
([(2,3)],4)
=> ([(0,1)],2)
=> 2
([(1,2),(1,3)],4)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 3
([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> 1
([(1,3),(2,3)],4)
=> ([],1)
=> 1
([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> 2
([],5)
=> ([],1)
=> 1
([(3,4)],5)
=> ([(0,1)],2)
=> 2
([(2,3),(2,4)],5)
=> ([],1)
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([],1)
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> 2
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 3
([(1,4),(4,2),(4,3)],5)
=> ([],1)
=> 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> 1
([(2,4),(3,4)],5)
=> ([],1)
=> 1
([(1,4),(2,4),(4,3)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> 2
([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 8
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 8
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 8
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ? = 8
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 8
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 8
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ? = 10
([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ? = 8
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ? = 16
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
=> ([(0,5),(0,6),(1,9),(2,8),(3,10),(4,11),(5,3),(5,13),(6,4),(6,13),(8,7),(9,7),(10,2),(10,12),(11,1),(11,12),(12,8),(12,9),(13,10),(13,11)],14)
=> ? = 14
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
=> ([(0,3),(0,4),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(7,5),(7,6),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 12
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ? = 8
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
=> ? = 10
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
=> ([(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(8,9),(8,10),(9,11),(10,11),(11,3),(11,4)],12)
=> ? = 12
([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ? = 8
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ? = 8
([(0,7),(1,6),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ? = 16
([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 9
([(2,5),(3,4),(4,6),(5,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 9
Description
The number of left modular elements of a lattice.
A pair $(x, y)$ of elements of a lattice $L$ is a modular pair if for every $z\geq y$ we have that $(y\vee x) \wedge z = y \vee (x \wedge z)$. An element $x$ is left-modular if $(x, y)$ is a modular pair for every $y\in L$.
Matching statistic: St001318
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(1,2),(1,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(1,4),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 8
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 8
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(4,7),(5,6)],8)
=> ? = 8
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ?
=> ?
=> ? = 16
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
=> ([(0,5),(0,6),(1,9),(2,8),(3,10),(4,11),(5,3),(5,13),(6,4),(6,13),(8,7),(9,7),(10,2),(10,12),(11,1),(11,12),(12,8),(12,9),(13,10),(13,11)],14)
=> ?
=> ?
=> ? = 14
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
=> ([(0,3),(0,4),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(7,5),(7,6),(8,9),(8,10),(9,11),(10,11)],12)
=> ?
=> ?
=> ? = 12
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(4,7),(5,6)],8)
=> ? = 8
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
=> ?
=> ?
=> ? = 10
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
=> ([(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(8,9),(8,10),(9,11),(10,11),(11,3),(11,4)],12)
=> ?
=> ?
=> ? = 12
([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(4,7),(5,6)],8)
=> ? = 8
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,7),(1,6),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(2,5),(2,7),(2,8),(2,9),(2,11),(2,14),(2,15),(3,4),(3,6),(3,7),(3,9),(3,11),(3,13),(3,15),(4,6),(4,7),(4,8),(4,11),(4,12),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(6,7),(6,10),(6,14),(6,15),(7,10),(7,12),(7,13),(8,9),(8,10),(8,13),(8,15),(9,10),(9,12),(9,14),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(11,15),(12,13),(12,14),(12,15),(13,14),(13,15),(14,15)],16)
=> ? = 16
([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(2,5),(3,4),(4,6),(5,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
Description
The number of vertices of the largest induced subforest with the same number of connected components of a graph.
Matching statistic: St001321
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(1,2),(1,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(1,4),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 8
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 8
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(4,7),(5,6)],8)
=> ? = 8
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ?
=> ?
=> ? = 16
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
=> ([(0,5),(0,6),(1,9),(2,8),(3,10),(4,11),(5,3),(5,13),(6,4),(6,13),(8,7),(9,7),(10,2),(10,12),(11,1),(11,12),(12,8),(12,9),(13,10),(13,11)],14)
=> ?
=> ?
=> ? = 14
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
=> ([(0,3),(0,4),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(7,5),(7,6),(8,9),(8,10),(9,11),(10,11)],12)
=> ?
=> ?
=> ? = 12
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(4,7),(5,6)],8)
=> ? = 8
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
=> ?
=> ?
=> ? = 10
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
=> ([(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(8,9),(8,10),(9,11),(10,11),(11,3),(11,4)],12)
=> ?
=> ?
=> ? = 12
([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(4,7),(5,6)],8)
=> ? = 8
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,7),(1,6),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(2,5),(2,7),(2,8),(2,9),(2,11),(2,14),(2,15),(3,4),(3,6),(3,7),(3,9),(3,11),(3,13),(3,15),(4,6),(4,7),(4,8),(4,11),(4,12),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(6,7),(6,10),(6,14),(6,15),(7,10),(7,12),(7,13),(8,9),(8,10),(8,13),(8,15),(9,10),(9,12),(9,14),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(11,15),(12,13),(12,14),(12,15),(13,14),(13,15),(14,15)],16)
=> ? = 16
([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(2,5),(3,4),(4,6),(5,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
Description
The number of vertices of the largest induced subforest of a graph.
Matching statistic: St001342
Values
([],1)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([],2)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(1,2),(1,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(2,3)],4)
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([],3)
=> 3
([(1,4),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([],1)
=> 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 8
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(4,7),(5,6),(6,7)],8)
=> ? = 8
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 8
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(4,7),(5,6)],8)
=> ? = 8
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ?
=> ?
=> ? = 16
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
=> ([(0,5),(0,6),(1,9),(2,8),(3,10),(4,11),(5,3),(5,13),(6,4),(6,13),(8,7),(9,7),(10,2),(10,12),(11,1),(11,12),(12,8),(12,9),(13,10),(13,11)],14)
=> ?
=> ?
=> ? = 14
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
=> ([(0,3),(0,4),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(7,5),(7,6),(8,9),(8,10),(9,11),(10,11)],12)
=> ?
=> ?
=> ? = 12
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)
=> ? = 10
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(4,7),(5,6)],8)
=> ? = 8
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
=> ?
=> ?
=> ? = 10
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
=> ([(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(8,9),(8,10),(9,11),(10,11),(11,3),(11,4)],12)
=> ?
=> ?
=> ? = 12
([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(4,7),(5,6)],8)
=> ? = 8
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6)],8)
=> ? = 8
([(0,7),(1,6),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(2,5),(2,7),(2,8),(2,9),(2,11),(2,14),(2,15),(3,4),(3,6),(3,7),(3,9),(3,11),(3,13),(3,15),(4,6),(4,7),(4,8),(4,11),(4,12),(4,14),(5,6),(5,8),(5,9),(5,11),(5,12),(5,13),(6,7),(6,10),(6,14),(6,15),(7,10),(7,12),(7,13),(8,9),(8,10),(8,13),(8,15),(9,10),(9,12),(9,14),(10,11),(10,12),(10,13),(10,14),(10,15),(11,12),(11,13),(11,14),(11,15),(12,13),(12,14),(12,15),(13,14),(13,15),(14,15)],16)
=> ? = 16
([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
([(2,5),(3,4),(4,6),(5,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 9
Description
The number of vertices in the center of a graph.
The center of a graph is the set of vertices whose maximal distance to any other vertex is minimal. In particular, if the graph is disconnected, all vertices are in the certer.
Matching statistic: St001622
Values
([],1)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([],2)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([],3)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(1,2)],3)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([(0,1),(0,2)],3)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 3
([(0,2),(1,2)],3)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([],4)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([(1,2),(1,3)],4)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 3
([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 4
([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 3
([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(3,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,1),(0,2),(0,3),(0,4)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(1,3),(1,4),(4,2)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 3
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> ([(0,3),(2,1),(3,2)],4)
=> 3
([(1,4),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,4),(1,4),(2,3)],5)
=> ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,2),(2,1)],3)
=> 2
([(0,4),(1,3),(2,3),(2,4)],5)
=> ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 1
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
=> ([(0,8),(2,13),(3,11),(4,9),(5,10),(6,3),(6,10),(7,4),(7,12),(8,5),(8,6),(9,13),(10,7),(10,11),(11,12),(12,2),(12,9),(13,1)],14)
=> ? = 8
([(0,5),(1,4),(4,2),(5,3)],6)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
=> ? = 9
([(0,5),(1,4),(2,3)],6)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,2),(2,6),(2,7),(2,8),(3,17),(4,16),(5,15),(6,12),(6,13),(7,12),(7,14),(8,13),(8,14),(9,19),(10,19),(11,19),(12,5),(12,18),(13,4),(13,18),(14,3),(14,18),(15,9),(15,10),(16,9),(16,11),(17,10),(17,11),(18,15),(18,16),(18,17),(19,1)],20)
=> ? = 8
([(0,5),(1,3),(4,2),(5,4)],6)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
=> ? = 8
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,2),(2,6),(2,7),(2,8),(3,17),(4,16),(5,15),(6,12),(6,13),(7,12),(7,14),(8,13),(8,14),(9,19),(10,19),(11,19),(12,5),(12,18),(13,4),(13,18),(14,3),(14,18),(15,9),(15,10),(16,9),(16,11),(17,10),(17,11),(18,15),(18,16),(18,17),(19,1)],20)
=> ? = 8
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ?
=> ? = 10
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(2,10),(3,11),(4,9),(5,4),(5,11),(6,1),(7,8),(8,3),(8,5),(9,10),(10,6),(11,2),(11,9)],12)
=> ? = 8
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
=> ([(0,7),(2,10),(3,11),(4,9),(5,4),(5,11),(6,1),(7,8),(8,3),(8,5),(9,10),(10,6),(11,2),(11,9)],12)
=> ? = 8
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,2),(2,6),(2,7),(2,8),(3,17),(4,16),(5,15),(6,12),(6,13),(7,12),(7,14),(8,13),(8,14),(9,19),(10,19),(11,19),(12,5),(12,18),(13,4),(13,18),(14,3),(14,18),(15,9),(15,10),(16,9),(16,11),(17,10),(17,11),(18,15),(18,16),(18,17),(19,1)],20)
=> ? = 8
([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
=> ? = 8
([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
=> ? = 9
([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(0,8),(1,14),(3,13),(4,12),(5,11),(6,7),(6,12),(7,5),(7,9),(8,4),(8,6),(9,11),(9,13),(10,14),(11,10),(12,3),(12,9),(13,1),(13,10),(14,2)],15)
=> ? = 8
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,2),(2,6),(2,7),(2,8),(3,17),(4,16),(5,15),(6,12),(6,13),(7,12),(7,14),(8,13),(8,14),(9,19),(10,19),(11,19),(12,5),(12,18),(13,4),(13,18),(14,3),(14,18),(15,9),(15,10),(16,9),(16,11),(17,10),(17,11),(18,15),(18,16),(18,17),(19,1)],20)
=> ? = 8
([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
=> ? = 9
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,2),(5,3)],8)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
=> ?
=> ? = 10
([(0,3),(0,7),(1,2),(1,6),(2,7),(3,6),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,4),(0,5),(1,6),(2,6),(4,7),(5,7),(6,3),(7,1),(7,2)],8)
=> ([(0,8),(2,9),(3,9),(4,10),(5,10),(6,1),(7,4),(7,5),(8,2),(8,3),(9,7),(10,6)],11)
=> ? = 8
([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
=> ?
=> ?
=> ? = 16
([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8)
=> ([(0,5),(0,6),(1,9),(2,8),(3,10),(4,11),(5,3),(5,13),(6,4),(6,13),(8,7),(9,7),(10,2),(10,12),(11,1),(11,12),(12,8),(12,9),(13,10),(13,11)],14)
=> ?
=> ?
=> ? = 14
([(0,5),(0,7),(1,4),(1,6),(4,7),(5,6),(6,2),(7,3)],8)
=> ([(0,3),(0,4),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(7,5),(7,6),(8,9),(8,10),(9,11),(10,11)],12)
=> ?
=> ?
=> ? = 12
([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(6,4),(7,5)],8)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
=> ?
=> ? = 10
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(6,3),(6,5),(7,2),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
=> ([(0,6),(1,10),(2,10),(4,9),(5,9),(6,7),(7,4),(7,5),(8,1),(8,2),(9,8),(10,3)],11)
=> ? = 8
([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8)
=> ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
=> ?
=> ?
=> ? = 10
([(0,5),(1,4),(2,7),(3,6),(4,2),(4,6),(5,3),(5,7)],8)
=> ([(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,2),(5,8),(6,1),(6,8),(8,9),(8,10),(9,11),(10,11),(11,3),(11,4)],12)
=> ?
=> ?
=> ? = 12
([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
=> ([(0,8),(2,10),(3,10),(4,9),(5,9),(6,7),(7,2),(7,3),(8,4),(8,5),(9,6),(10,1)],11)
=> ? = 8
([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
=> ([(0,2),(2,6),(2,7),(2,8),(3,17),(4,16),(5,15),(6,12),(6,13),(7,12),(7,14),(8,13),(8,14),(9,19),(10,19),(11,19),(12,5),(12,18),(13,4),(13,18),(14,3),(14,18),(15,9),(15,10),(16,9),(16,11),(17,10),(17,11),(18,15),(18,16),(18,17),(19,1)],20)
=> ? = 8
([(0,7),(1,6),(2,5),(3,4)],8)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ([(0,1),(0,2),(0,3),(0,4),(1,8),(1,9),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,9),(4,5),(4,6),(4,8),(5,11),(5,14),(6,11),(6,12),(7,11),(7,13),(8,12),(8,14),(9,13),(9,14),(10,12),(10,13),(11,15),(12,15),(13,15),(14,15)],16)
=> ?
=> ? = 16
([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
=> ? = 9
([(2,5),(3,4),(4,6),(5,7)],8)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
=> ? = 9
Description
The number of join-irreducible elements of a lattice.
An element $j$ of a lattice $L$ is '''join irreducible''' if it is not the least element and if $j=x\vee y$, then $j\in\{x,y\}$ for all $x,y\in L$.
The following 22 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001717The largest size of an interval in a poset. St001300The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset. St000189The number of elements in the poset. St001615The number of join prime elements of a lattice. St001617The dimension of the space of valuations of a lattice. St000363The number of minimal vertex covers of a graph. St000993The multiplicity of the largest part of an integer partition. St000070The number of antichains in a poset. St000656The number of cuts of a poset. St001875The number of simple modules with projective dimension at most 1. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000777The number of distinct eigenvalues of the distance Laplacian of a connected graph. St001645The pebbling number of a connected graph. St000259The diameter of a connected graph. St000260The radius of a connected graph. St000302The determinant of the distance matrix of a connected graph. St000466The Gutman (or modified Schultz) index of a connected graph. St000467The hyper-Wiener index of a connected graph. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice. St001879The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
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