ToLehmerCode

Entry i counts the later entries smaller than p(i).

WikipediaLehmer code↗WikidataQ2981462↗Rosetta CodePermutations/Rank of a permutation↗

ToLehmerCode(Permutation)Entry i counts the later entries smaller than p(i).

Typed signatures

Type	Package	Applies
(permutation) -> permutation_inversion	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a Permutation and returns a PermutationInversion — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• Its total is the inversion count, which is the Lehmer code's whole point.

Examples

Basic #

the one-line word $231$

live ↗

In$\mathrm{ToLehmerCode}({\operatorname{Permutation}}([2, 3, 1]))$Out${\operatorname{PermutationInversion}}([1, 1, 0])$

About

Examples	1
Crosswalk	WikipediaWikidataRosetta Code