LongestRun

The length of the longest run of consecutive increases.

LongestRun(p)The length of the longest run of consecutive increases.

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.
• Expressed with Fold — which compute-engine does have, contrary to what an earlier version of this package claimed when it put this statistic on the frontier.

Definition

Epsil, as the implementation runs it.

on Permutation, over _x

0 if Length(_x) < 1 else Fold(
                               Function(
                                         [Max([a[1], a[2] + 1]), a[2] + 1, b] if b > a[3] else [Max([a[1], 1]), 1, b],
                                         a,
                                         b,
                                       ),
                               [0, 0, 0],
                               _x,
                             )[1]

Examples

Basic #

the one-line word $312$

live ↗

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

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

live ↗

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

the one-line word $2413$

live ↗

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

About

Examples	3