Identifier
Values
0 => ([(0,1)],2) => ([],2) => 1
1 => ([(0,1)],2) => ([],2) => 1
00 => ([(0,2),(2,1)],3) => ([],3) => 1
01 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 2
10 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 2
11 => ([(0,2),(2,1)],3) => ([],3) => 1
000 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 3
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 2
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 3
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 3
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 2
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 3
111 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 1
0001 => ([(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) => 4
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => ([(2,7),(3,6),(4,5)],8) => 3
0111 => ([(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) => 4
1000 => ([(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) => 4
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => ([(2,7),(3,6),(4,5)],8) => 3
1110 => ([(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) => 4
1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 1
000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 1
111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 1
0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([],8) => 1
1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([],8) => 1
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Description
The achromatic number of a graph.
This is the maximal number of colours of a proper colouring, such that for any pair of colours there are two adjacent vertices with these colours.
Map
poset of factors
Description
The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.
Map
incomparability graph
Description
The incomparability graph of a poset.