Convexity

The largest 2 p(i) - p(i-1) - p(i+1) over the interior positions, or 0.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000226via Permutation✓↗

Convexity(p)The largest 2 p(i) - p(i-1) - p(i+1) over the interior positions, or 0.

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) < 3 else Max(Join([0], Map(
                                            Function(2 * _x[i] - _x[i - 1] -
                                                     _x[i + 1], i),
                                            Range(2, Length(_x) - 1),
                                          )))

Examples

Basic #

the one-line word $312$

live ↗

In$\mathrm{Convexity}({\operatorname{Permutation}}([3, 1, 2]))$Out$0$

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

live ↗

In$\mathrm{Convexity}(\bigl\lbrack3, 1, 2\bigr\rbrack)$Out$0$

the one-line word $2413$

live ↗

In$\mathrm{Convexity}({\operatorname{Permutation}}([2, 4, 1, 3]))$Out$5$

Properties #

FindStat's value for [1,2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1, 2]), \text{Convexity})$Out$0$

Known value · FindStat St000226

FindStat's value for [2,1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([2, 1]), \text{Convexity})$Out$0$

Known value · FindStat St000226

FindStat's value for [1,2,3]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1, 2, 3]), \text{Convexity})$Out$0$

Known value · FindStat St000226

About

Examples	6
Crosswalk	FindStat