AlternatingComplement

Every second letter swapped for the other, starting with the second.

FindStatMp00158via BinaryWord↗

AlternatingComplement(BinaryWord)Every second letter swapped for the other, starting with the second.

Typed signatures

Type	Package	Applies
(binary_word) -> binary_word	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a BinaryWord and returns a BinaryWord — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00158, "alternating inverse", an involution.

Examples

Basic #

the binary word $01100$

live ↗

In$\mathrm{AlternatingComplement}({\operatorname{BinaryWord}}([0, 1, 1, 0, 0]))$Out${\operatorname{BinaryWord}}([0, 0, 1, 1, 0])$

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Examples	1
Crosswalk	FindStat