Identifier
Values
[1,2] => 0 => ([(0,1)],2) => 1
[2,1] => 1 => ([(0,1)],2) => 1
[1,2,3] => 00 => ([(0,2),(2,1)],3) => 1
[1,3,2] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[2,1,3] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[2,3,1] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[3,1,2] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[3,2,1] => 11 => ([(0,2),(2,1)],3) => 1
[1,2,3,4] => 000 => ([(0,3),(2,1),(3,2)],4) => 1
[1,2,4,3] => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[1,3,2,4] => 010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2
[1,3,4,2] => 010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2
[1,4,2,3] => 010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2
[1,4,3,2] => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[2,1,3,4] => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[2,1,4,3] => 101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2
[2,3,1,4] => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[2,3,4,1] => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[2,4,1,3] => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[2,4,3,1] => 101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2
[3,1,2,4] => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[3,1,4,2] => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[3,2,1,4] => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[3,2,4,1] => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[3,4,1,2] => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[3,4,2,1] => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[4,1,2,3] => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[4,1,3,2] => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[4,2,1,3] => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[4,2,3,1] => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[4,3,1,2] => 101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 2
[4,3,2,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 1
[1,2,3,4,5] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,3,2,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[1,2,3,4,5,6] => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[6,5,4,3,2,1] => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[1,2,3,4,5,6,7] => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[7,6,5,4,3,2,1] => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
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Description
The maximal number of elements covering an element of a poset.
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.
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 $v$.