Lattice Path Enumeration and Its Applications in Representation Theory
arXiv:1708.07003
Abstract
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
arXiv admin note: substantial text overlap with arXiv:1610.04122