MinimalDyckPath

The shortest Dyck path tracing the shape of the Ferrers diagram.

FindStatMp00043via IntegerPartition↗

MinimalDyckPath(IntegerPartition)The shortest Dyck path tracing the shape of the Ferrers diagram.

Typed signatures

Type	Package	Applies
(integer_partition) -> dyck_path	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a IntegerPartition and returns a DyckPath — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00043, Sage's partition to minimal Dyck word. Injective: the partition is the region above the path, and this is the shortest path whose region it is.

Examples

Basic #

the partition $4 + 2 + 1$

live ↗

In$\mathrm{MinimalDyckPath}({\operatorname{IntegerPartition}}([4, 2, 1]))$Out${\operatorname{DyckPath}}([1, 1, 0, 1, 0, 1, 0, 0, 1, 0])$

About

Examples	1
Crosswalk	FindStat