DescentComposition

The composition of n cut at the descent positions.

FindStatMp00071via Permutation↗

DescentComposition(Permutation)The composition of n cut at the descent positions.

Typed signatures

Type	Package	Applies
(permutation) -> composition	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a Permutation and returns a IntegerComposition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• Its parts sum to n and its length is one more than Descents — another statistic readable off a map. Removed once for erroring on words with no descents; Range(1, 0) never evaluates, so the short case has to be stated.

Examples

Basic #

the one-line word $231$

live ↗

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

About

Examples	1
Crosswalk	FindStat