Peeling

The path whose area sequence is this one's with its first entry dropped and the rest lowered by two.

Peeling(DyckPath)The path whose area sequence is this one's with its first entry dropped and the rest lowered by two.

Typed signatures

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

Domain: Combinatorial maps

Details

Takes a DyckPath and returns a DyckPath — a typed map, so a wrong carrier is a type error rather than a wrong answer.
FindStat's Mp00103, the peeling map. Lossy: it is not injective, and a path of semilength n goes to one of the same semilength.

Examples

Basic #

the Dyck path $UUDDUD$

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

Out

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

About

Examples	1
Crosswalk	FindStat