OverlapSetSize

Shifts i < n for which the first n - i entries and the last n - i entries are in the same relative order.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001096via Permutation✓↗

OverlapSetSize(p)Shifts i < n for which the first n - i entries and the last n - i entries are in the same relative order.

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) < 2 else Count(Filter(
                                       Range(1, Length(_x) - 1),
                                       Function(Max(Sum(Map(
                                                             Function(Count(Filter(
                                                                                    Range(1, Length(_x) - i, 1),
                                                                                    Function(b > a &&
                                                                                             (-1 if _x[a] < _x[b] else 1 if _x[a] > _x[b] else 0) !=
                                                                                             (-1 if _x[a + i] <
                                                                                                    _x[b + i] else 1 if _x[a + i] >
                                                                                                               _x[b + i] else 0), b),
                                                                                  )), a),
                                                             Range(
                                                                    1,
                                                                    Length(_x) -
                                                                    i,
                                                                    1,
                                                                  ),
                                                           )), 0) == 0, i),
                                     ))

Examples

Basic #

the one-line word $312$

live ↗

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

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

live ↗

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

the one-line word $2413$

live ↗

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

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St001096

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St001096

FindStat's value for [2,1]

live ↗

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

Known value · FindStat St001096

About

Examples	6
Crosswalk	FindStat