LargestRunLength

The length of the longest increasing run (the catalog's second spelling of LongestRun).

LargestRunLength(p)The length of the longest increasing run (the catalog's second spelling of LongestRun).

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

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

live ↗

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

the one-line word $2413$

live ↗

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

About

Examples	3