Identifier
Values
0 => 0 => ([(0,1)],2) => -1
1 => 1 => ([(0,1)],2) => -1
00 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => -1
01 => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => -1
10 => 00 => ([(0,2),(2,1)],3) => -1
11 => 11 => ([(0,2),(2,1)],3) => -1
000 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
001 => 101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => -1
010 => 000 => ([(0,3),(2,1),(3,2)],4) => -1
011 => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
100 => 010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => -1
101 => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
110 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => -1
111 => 111 => ([(0,3),(2,1),(3,2)],4) => -1
1010 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => -1
1111 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => -1
01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => -1
11111 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => -1
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Description
The trace of the Coxeter matrix of the incidence algebra of a poset.
Map
flag zeros to zeros
Description
Return a binary word of the same length, such that the number of zeros equals the number of occurrences of $10$ in the word obtained from the original word by prepending the reverse of the complement.
For example, the image of the word $w=1\dots 1$ is $1\dots 1$, because $0\dots 01\dots 1$ has no occurrences of $10$. The words $10\dots 10$ and $010\dots 10$ have image $0\dots 0$.
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 $v$.