LongestSuccessionRun

The length of the longest factor p(k), ..., p(l) with p(i+1) = p(i) + 1.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001652via Permutation✓↗

LongestSuccessionRun(p)The length of the longest factor p(k), ..., p(l) with p(i+1) = p(i) + 1.

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.
• FindStat's St001662 reads the same, but its code miscounts runs that restart after a gap, so only St001652 is matched.

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] + 1 else [Max([a[1], 1]), 1, b],
                                        a,
                                        b,
                                      ), [0, 0, 0], _x)[1]

Examples

Basic #

the one-line word $312$

live ↗

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

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

live ↗

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

the one-line word $2413$

live ↗

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

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St001652

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St001652

FindStat's value for [2,1]

live ↗

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

Known value · FindStat St001652

About

Examples	6
Crosswalk	FindStat