Identifier
- St001958: Permutations ⟶ ℤ
Values
[1] => 0
[1,2] => 1
[2,1] => 1
[1,2,3] => 1
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 1
[1,2,3,4] => 1
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 3
[1,4,2,3] => 3
[1,4,3,2] => 3
[2,1,3,4] => 3
[2,1,4,3] => 3
[2,3,1,4] => 3
[2,3,4,1] => 3
[2,4,1,3] => 3
[2,4,3,1] => 3
[3,1,2,4] => 3
[3,1,4,2] => 3
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 3
[3,4,2,1] => 3
[4,1,2,3] => 3
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 3
[4,3,1,2] => 3
[4,3,2,1] => 1
[1,2,3,4,5] => 1
[1,2,3,5,4] => 4
[1,2,4,3,5] => 4
[1,2,4,5,3] => 3
[1,2,5,3,4] => 4
[1,2,5,4,3] => 4
[1,3,2,4,5] => 4
[1,3,2,5,4] => 4
[1,3,4,2,5] => 4
[1,3,4,5,2] => 4
[1,3,5,2,4] => 4
[1,3,5,4,2] => 4
[1,4,2,3,5] => 4
[1,4,2,5,3] => 4
[1,4,3,2,5] => 3
[1,4,3,5,2] => 4
[1,4,5,2,3] => 4
[1,4,5,3,2] => 4
[1,5,2,3,4] => 4
[1,5,2,4,3] => 4
[1,5,3,2,4] => 4
[1,5,3,4,2] => 4
[1,5,4,2,3] => 3
[1,5,4,3,2] => 4
[2,1,3,4,5] => 4
[2,1,3,5,4] => 3
[2,1,4,3,5] => 4
[2,1,4,5,3] => 4
[2,1,5,3,4] => 4
[2,1,5,4,3] => 4
[2,3,1,4,5] => 4
[2,3,1,5,4] => 4
[2,3,4,1,5] => 4
[2,3,4,5,1] => 4
[2,3,5,1,4] => 4
[2,3,5,4,1] => 4
[2,4,1,3,5] => 4
[2,4,1,5,3] => 4
[2,4,3,1,5] => 4
[2,4,3,5,1] => 4
[2,4,5,1,3] => 4
[2,4,5,3,1] => 4
[2,5,1,3,4] => 4
[2,5,1,4,3] => 4
[2,5,3,1,4] => 3
[2,5,3,4,1] => 4
[2,5,4,1,3] => 4
[2,5,4,3,1] => 4
[3,1,2,4,5] => 3
[3,1,2,5,4] => 4
[3,1,4,2,5] => 4
[3,1,4,5,2] => 4
[3,1,5,2,4] => 4
[3,1,5,4,2] => 4
[3,2,1,4,5] => 4
[3,2,1,5,4] => 4
[3,2,4,1,5] => 4
[3,2,4,5,1] => 3
[3,2,5,1,4] => 4
[3,2,5,4,1] => 4
[3,4,1,2,5] => 4
[3,4,1,5,2] => 4
[3,4,2,1,5] => 3
[3,4,2,5,1] => 4
[3,4,5,1,2] => 4
[3,4,5,2,1] => 4
[3,5,1,2,4] => 4
[3,5,1,4,2] => 4
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Description
The degree of the polynomial interpolating the values of a permutation.
Given a permutation $\pi\in\mathfrak S_n$ there is a polynomial $p$ of minimal degree such that $p(n)=\pi(n)$ for $n\in\{1,\dots,n\}$.
This statistic records the degree of $p$.
Given a permutation $\pi\in\mathfrak S_n$ there is a polynomial $p$ of minimal degree such that $p(n)=\pi(n)$ for $n\in\{1,\dots,n\}$.
This statistic records the degree of $p$.
Code
def statistic(pi):
R = PolynomialRing(QQ, "n")
return R.lagrange_polynomial(list(enumerate(pi))).degree()
Created
Sep 30, 2024 at 14:23 by Martin Rubey
Updated
Sep 30, 2024 at 14:23 by Martin Rubey
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