Identifier
-
Mp00317:
Integer partitions
—odd parts⟶
Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St001668: Posets ⟶ ℤ
Values
[1] => 1 => ([(0,1)],2) => 1
[2] => 0 => ([(0,1)],2) => 1
[1,1] => 11 => ([(0,2),(2,1)],3) => 2
[3] => 1 => ([(0,1)],2) => 1
[2,1] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,1,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[4] => 0 => ([(0,1)],2) => 1
[3,1] => 11 => ([(0,2),(2,1)],3) => 2
[2,2] => 00 => ([(0,2),(2,1)],3) => 2
[1,1,1,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[5] => 1 => ([(0,1)],2) => 1
[4,1] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[3,2] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[3,1,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[6] => 0 => ([(0,1)],2) => 1
[5,1] => 11 => ([(0,2),(2,1)],3) => 2
[4,2] => 00 => ([(0,2),(2,1)],3) => 2
[3,3] => 11 => ([(0,2),(2,1)],3) => 2
[3,1,1,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[2,2,2] => 000 => ([(0,3),(2,1),(3,2)],4) => 3
[7] => 1 => ([(0,1)],2) => 1
[6,1] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[5,2] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[5,1,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[4,3] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[3,3,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[8] => 0 => ([(0,1)],2) => 1
[7,1] => 11 => ([(0,2),(2,1)],3) => 2
[6,2] => 00 => ([(0,2),(2,1)],3) => 2
[5,3] => 11 => ([(0,2),(2,1)],3) => 2
[5,1,1,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[4,4] => 00 => ([(0,2),(2,1)],3) => 2
[4,2,2] => 000 => ([(0,3),(2,1),(3,2)],4) => 3
[3,3,1,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[2,2,2,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[9] => 1 => ([(0,1)],2) => 1
[8,1] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[7,2] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[7,1,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[6,3] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[5,4] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[5,3,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[3,3,3] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[10] => 0 => ([(0,1)],2) => 1
[9,1] => 11 => ([(0,2),(2,1)],3) => 2
[8,2] => 00 => ([(0,2),(2,1)],3) => 2
[7,3] => 11 => ([(0,2),(2,1)],3) => 2
[7,1,1,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[6,4] => 00 => ([(0,2),(2,1)],3) => 2
[6,2,2] => 000 => ([(0,3),(2,1),(3,2)],4) => 3
[5,5] => 11 => ([(0,2),(2,1)],3) => 2
[5,3,1,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[4,4,2] => 000 => ([(0,3),(2,1),(3,2)],4) => 3
[4,2,2,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[3,3,3,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[11] => 1 => ([(0,1)],2) => 1
[10,1] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[9,2] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[9,1,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[8,3] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[7,4] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[7,3,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[6,5] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[5,5,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[5,3,3] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[12] => 0 => ([(0,1)],2) => 1
[11,1] => 11 => ([(0,2),(2,1)],3) => 2
[10,2] => 00 => ([(0,2),(2,1)],3) => 2
[9,3] => 11 => ([(0,2),(2,1)],3) => 2
[9,1,1,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[8,4] => 00 => ([(0,2),(2,1)],3) => 2
[8,2,2] => 000 => ([(0,3),(2,1),(3,2)],4) => 3
[7,5] => 11 => ([(0,2),(2,1)],3) => 2
[7,3,1,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[6,6] => 00 => ([(0,2),(2,1)],3) => 2
[6,4,2] => 000 => ([(0,3),(2,1),(3,2)],4) => 3
[6,2,2,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[5,5,1,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[5,3,3,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[4,4,4] => 000 => ([(0,3),(2,1),(3,2)],4) => 3
[4,4,2,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[3,3,3,3] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[13] => 1 => ([(0,1)],2) => 1
[12,1] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[11,2] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[11,1,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[10,3] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[9,4] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[9,3,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[8,5] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[7,6] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[7,5,1] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[7,3,3] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[5,5,3] => 111 => ([(0,3),(2,1),(3,2)],4) => 3
[14] => 0 => ([(0,1)],2) => 1
[13,1] => 11 => ([(0,2),(2,1)],3) => 2
[12,2] => 00 => ([(0,2),(2,1)],3) => 2
[11,3] => 11 => ([(0,2),(2,1)],3) => 2
[11,1,1,1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[10,4] => 00 => ([(0,2),(2,1)],3) => 2
[10,2,2] => 000 => ([(0,3),(2,1),(3,2)],4) => 3
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Description
The number of points of the poset minus the width of the poset.
Map
odd parts
Description
Return the binary word indicating which parts of the partition are odd.
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 $v$.
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 $v$.
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