CutOutPartition

The partition cut out of the staircase by the path: part i is the number of downs before the (n + 1 - i)-th up step.

FindStatMp00027via DyckPath↗

CutOutPartition(DyckPath)The partition cut out of the staircase by the path: part i is the number of downs before the (n + 1 - i)-th up step.

Typed signatures

Type	Package	Applies
(dyck_path) -> integer_partition	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a DyckPath and returns a IntegerPartition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00027, "to partition". Injective: its image is the partitions inside the staircase (n-1, ..., 1).

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

In$\mathrm{CutOutPartition}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))$Out${\operatorname{IntegerPartition}}([2])$

About

Examples	1
Crosswalk	FindStat