ReverseComplement

Reverse, then complement.

ReverseComplement(Permutation)Reverse, then complement.

Typed signatures

Type	Package	Applies
`((dyck_path) -> dyck_path) & ((permutation) -> permutation)`	`combinatorics`	always

Domain: Combinatorial maps

Details

Takes a Permutation and returns a Permutation — a typed map, so a wrong carrier is a type error rather than a wrong answer.
Defined as a COMPOSITION, applied right to left: Complement after Reverse. Each step goes through its own declared head, so every intermediate value is a properly constructed carrier.
A thin alias over Compose(Complement, Reverse). The catalog has the name, so we keep it — but the name is not what makes it work, and nothing stops a reader writing the composition directly.
Also takes a DyckPath, returning a DyckPath: The path read backwards, with ups and downs swapped: its mirror image across the vertical.
FindStat's "reverse" for Dyck paths: reading the steps backwards alone would leave the word's ups and downs unbalanced, so each step is also swapped.

Examples

Basic #

the one-line word $231$

\mathrm{ReverseComplement}({\operatorname{Permutation}}([2, 3, 1]))

Out

{\operatorname{Permutation}}([3, 1, 2])

the Dyck path $UUDDUD$

\mathrm{ReverseComplement}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))

Out

{\operatorname{DyckPath}}([1, 0, 1, 1, 0, 0])

About

Examples	2
Crosswalk	FindStat