A new poset for compositions equivalent to the Bruhat order of the symmetric group

A new poset for compositions equivalent to the Bruhat order of the symmetric group

Lehmer's code gives a bijection between the symmetric group and the set of staircase compositions. In this paper, we define a new poset for such compositions and derive its equivalence with the strong Bruhat order of the symmetric group. This is an intrinsic construction that does not require a...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2022-02
Hauptverfasser: Lambert, Jordan, Lonardo Rabelo
Format: Artikel
Sprache:eng
Schlagworte:
Composition
Equivalence
Group theory
Permutations
Set theory
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Lehmer's code gives a bijection between the symmetric group and the set of staircase compositions. In this paper, we define a new poset for such compositions and derive its equivalence with the strong Bruhat order of the symmetric group. This is an intrinsic construction that does not require any mention of the associated permutations.
ISSN:2331-8422