ConnectivityWord

Letter i is 1 when the first i entries are all smaller than the rest: the connectivity set as a binary word.

FindStatMp00114via Permutation↗

ConnectivityWord(Permutation)Letter i is 1 when the first i entries are all smaller than the rest: the connectivity set as a binary word.

Typed signatures

Type	Package	Applies
(permutation) -> binary_word	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a Permutation and returns a BinaryWord — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00114. One letter shorter than the permutation; the word is all 0 exactly when the permutation is connected.

Examples

Basic #

the one-line word $231$

live ↗

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

About

Examples	1
Crosswalk	FindStat