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Lattice Path Enumeration and Its Applications in Representation Theory (1708.07003v1)
Published 22 Aug 2017 in math.CO
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
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