Identifier
Values
0 => 0 => ([(0,1)],2) => ([],2) => 0
1 => 1 => ([(0,1)],2) => ([],2) => 0
00 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
01 => 00 => ([(0,2),(2,1)],3) => ([],3) => 0
10 => 11 => ([(0,2),(2,1)],3) => ([],3) => 0
11 => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
000 => 010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 2
001 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 0
010 => 000 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
011 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 0
100 => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 0
101 => 111 => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
110 => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 0
111 => 101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 2
0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 0
101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 0
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Description
The number of series nodes in the modular decomposition of a graph.
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.
Map
alternating inverse
Description
Sends a binary word $w_1\cdots w_m$ to the binary word $v_1 \cdots v_m$ with $v_i = w_i$ if $i$ is odd and $v_i = 1 - w_i$ if $i$ is even.
This map is used in [1], see Definitions 3.2 and 5.1.