CodeComposition

The composition whose code is the word with a 1 put in front: each 1 opens a part, of 1 plus the zeros after it.

FindStatMp00178via BinaryWord↗

CodeComposition(BinaryWord)The composition whose code is the word with a 1 put in front: each 1 opens a part, of 1 plus the zeros after it.

Typed signatures

Type	Package	Applies
(binary_word) -> composition	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a BinaryWord and returns a IntegerComposition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00178, Sage's from_code. An injection one size up (the empty composition has no preimage); the inverse of CodeWord on the words that start with 1. Not IntegerComposition, whose word marks the cuts.

Examples

Basic #

the binary word $01100$

live ↗

In$\mathrm{CodeComposition}({\operatorname{BinaryWord}}([0, 1, 1, 0, 0]))$Out${\operatorname{IntegerComposition}}([2, 1, 3])$

About

Examples	1
Crosswalk	FindStat