Lattice Path Enumeration and Its Applications in Representation Theory

Lattice Path Enumeration and Its Applications in Representation Theory

In this paper, we enumerate lattice paths with certain constraints and apply the corresponding results to develop formulas for calculating the dimensions of submodules of a class of modules for planar upper triangular rook monoids. In particular, we show that the famous Catalan numbers appear as the...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2017-08
Hauptverfasser: Feng, Jianqiang, Liu, Wenli, Bai, Ximei, Li, Zhenheng
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Enumeration
Modules
Monoids
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In this paper, we enumerate lattice paths with certain constraints and apply the corresponding results to develop formulas for calculating the dimensions of submodules of a class of modules for planar upper triangular rook monoids. In particular, we show that the famous Catalan numbers appear as the dimensions of some special modules; we also obtain some combinatorial identities
ISSN:2331-8422