RepeatedLehmerCodeEntries

The Lehmer code's length less its number of distinct entries.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001298via Permutation✓↗

RepeatedLehmerCodeEntries(p)The Lehmer code's length less its number of distinct entries.

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 Length(_x) - Count(Filter(
                                                    Range(0, Length(_x) - 1, 1),
                                                    Function(Count(Filter(
                                                                           Range(1, Length(_x)),
                                                                           Function(Count(Filter(
                                                                                                  Range(i + 1, Length(_x), 1),
                                                                                                  Function(_x[j] < _x[i], j),
                                                                                                )) ==
                                                                                    v, i),
                                                                         )) > 0, v),
                                                  ))

Examples

Basic #

the one-line word $312$

live ↗

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

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

live ↗

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

the one-line word $2413$

live ↗

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

Properties #

FindStat's value for [1]

live ↗

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

Known value · FindStat St001298

FindStat's value for [1,2]

live ↗

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

Known value · FindStat St001298

FindStat's value for [2,1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([2, 1]), \text{RepeatedLehmerCodeEntries})$Out$0$

Known value · FindStat St001298

About

Examples	6
Crosswalk	FindStat