Identifier
Values
0 => 1 => ([(0,1)],2) => 1
1 => 0 => ([(0,1)],2) => 1
00 => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
01 => 11 => ([(0,2),(2,1)],3) => 1
10 => 00 => ([(0,2),(2,1)],3) => 1
11 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
000 => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
001 => 101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1
010 => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
011 => 111 => ([(0,3),(2,1),(3,2)],4) => 1
100 => 000 => ([(0,3),(2,1),(3,2)],4) => 1
101 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
110 => 010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1
111 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
0111 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
1000 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
01111 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
10000 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
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Description
The number of loops of the quiver corresponding to the reduced incidence algebra of a poset.
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
twist
Description
Return the binary word with first letter inverted.