MaximalSuccessiveDifference

The largest p(i+1) - p(i), negative for a decreasing permutation.

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MaximalSuccessiveDifference(p)The largest p(i+1) - p(i), negative for a decreasing permutation.

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.
• MaximalRiseSize is the same with a floor of 0.

Definition

Epsil, as the implementation runs it.

on Permutation, over _x

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

Examples

Basic #

the one-line word $312$

live ↗

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

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

live ↗

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

the one-line word $2413$

live ↗

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

Properties #

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St000652

FindStat's value for [2,1]

live ↗

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

Known value · FindStat St000652

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

live ↗

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

Known value · FindStat St000652

About

Examples	6
Crosswalk	FindStat