Identifier
Values
[1] => 0 => ([(0,1)],2) => 1
[-1] => 1 => ([(0,1)],2) => 1
[1,2] => 00 => ([(0,2),(2,1)],3) => 1
[1,-2] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[-1,2] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[-1,-2] => 11 => ([(0,2),(2,1)],3) => 1
[2,1] => 00 => ([(0,2),(2,1)],3) => 1
[2,-1] => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[-2,1] => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[-2,-1] => 11 => ([(0,2),(2,1)],3) => 1
[1,2,3] => 000 => ([(0,3),(2,1),(3,2)],4) => 1
[-1,-2,-3] => 111 => ([(0,3),(2,1),(3,2)],4) => 1
[1,3,2] => 000 => ([(0,3),(2,1),(3,2)],4) => 1
[-1,-3,-2] => 111 => ([(0,3),(2,1),(3,2)],4) => 1
[2,1,3] => 000 => ([(0,3),(2,1),(3,2)],4) => 1
[-2,-1,-3] => 111 => ([(0,3),(2,1),(3,2)],4) => 1
[2,3,1] => 000 => ([(0,3),(2,1),(3,2)],4) => 1
[-2,-3,-1] => 111 => ([(0,3),(2,1),(3,2)],4) => 1
[3,1,2] => 000 => ([(0,3),(2,1),(3,2)],4) => 1
[-3,-1,-2] => 111 => ([(0,3),(2,1),(3,2)],4) => 1
[3,2,1] => 000 => ([(0,3),(2,1),(3,2)],4) => 1
[-3,-2,-1] => 111 => ([(0,3),(2,1),(3,2)],4) => 1
[1,2,3,4] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-1,-2,-3,-4] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[1,2,4,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-1,-2,-4,-3] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[1,3,2,4] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-1,-3,-2,-4] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[1,3,4,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-1,-3,-4,-2] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[1,4,2,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-1,-4,-2,-3] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[1,4,3,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-1,-4,-3,-2] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,1,3,4] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-2,-1,-3,-4] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,1,4,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-2,-1,-4,-3] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,3,1,4] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-2,-3,-1,-4] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,3,4,1] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-2,-3,-4,-1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,4,1,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-2,-4,-1,-3] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,4,3,1] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-2,-4,-3,-1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,1,2,4] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-3,-1,-2,-4] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,1,4,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-3,-1,-4,-2] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,2,1,4] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-3,-2,-1,-4] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,2,4,1] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-3,-2,-4,-1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,4,1,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-3,-4,-1,-2] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,4,2,1] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-3,-4,-2,-1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,1,2,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-4,-1,-2,-3] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,1,3,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-4,-1,-3,-2] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,2,1,3] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-4,-2,-1,-3] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,2,3,1] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-4,-2,-3,-1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,3,1,2] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-4,-3,-1,-2] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,3,2,1] => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-4,-3,-2,-1] => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
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Description
The maximum magnitude of the Möbius function of a poset.
The Möbius function of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value $\mu(x, y)$ is equal to the signed sum of chains from $x$ to $y$, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the 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
signs
Description
The binary word recording the signs of a signed permutation.
This map sends a signed permutation $\pi\in\mathfrak H_n$ to the binary word $w$ of length $n$ such that $w_i = 0$ if $\pi(i) > 0$.