Ringel

The Ringel permutation of the Nakayama algebra whose Kupisch series the path gives, one size up.

FindStatMp00201via DyckPath↗

Ringel(DyckPath)The Ringel permutation of the Nakayama algebra whose Kupisch series the path gives, one size up.

Typed signatures

Type	Package	Applies
(dyck_path) -> permutation	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a DyckPath and returns a Permutation — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00201, after Ringel's The finitistic dimension of a Nakayama algebra. Injective, into the permutations of n + 1.

Examples

Basic #

the Dyck path $UUDDUD$

live ↗

In$\mathrm{Ringel}({\operatorname{DyckPath}}([1, 1, 0, 0, 1, 0]))$Out${\operatorname{Permutation}}([2, 4, 1, 3])$

About

Examples	1
Crosswalk	FindStat