InterpolatingPolynomialDegree

The degree of the polynomial through the points (i, p(i)): the largest k with a nonzero k-th finite difference.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001958via Permutation✓↗

InterpolatingPolynomialDegree(p)The degree of the polynomial through the points (i, p(i)): the largest k with a nonzero k-th finite difference.

Typed signatures

Type	Package	Applies
(list<integer> | permutation) -> number	combinatorics	always

Domain: Permutation statistics

Details

• Defined over Permutation as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a Permutation, and also a bare list of integers: this reading compares entries with each other rather than with their positions, so it stands on any sequence.

Definition

Epsil, as the implementation runs it.

on Permutation, over _x

0 if Length(_x) < 1 else Max(Filter(
                                     Range(0, Length(_x) - 1),
                                     Function(Sum(Map(
                                                       Function(Binomial(k, j) *
                                                                (1 if (k - j) %
                                                                      2 == 0 else -1) * _x[j + 1], j),
                                                       Range(0, k),
                                                     )) != 0, k),
                                   ))

Examples

Basic #

the one-line word $312$

live ↗

In$\mathrm{InterpolatingPolynomialDegree}({\operatorname{Permutation}}([3, 1, 2]))$Out$2$

the one-line word $312$, as a plain list

live ↗

In$\mathrm{InterpolatingPolynomialDegree}(\bigl\lbrack3, 1, 2\bigr\rbrack)$Out$2$

the one-line word $2413$

live ↗

In$\mathrm{InterpolatingPolynomialDegree}({\operatorname{Permutation}}([2, 4, 1, 3]))$Out$3$

Properties #

FindStat's value for [1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1]), \text{InterpolatingPolynomialDegree})$Out$0$

Known value · FindStat St001958

FindStat's value for [1,2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1, 2]), \text{InterpolatingPolynomialDegree})$Out$1$

Known value · FindStat St001958

FindStat's value for [2,1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([2, 1]), \text{InterpolatingPolynomialDegree})$Out$1$

Known value · FindStat St001958

About

Examples	6
Crosswalk	FindStat