A q-enumeration of lozenge tilings of a hexagon with four adjacent triangles removed from the boundary

2015/02/05 by Tri Lai, Lai, Tri
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models

paper · pdf · doi:10.48550/arxiv.1502.01679

Abstract

MacMahon proved a simple product formula for the generating function of plane partitions fitting in a given box. The theorem implies a q-enumeration of lozenge tilings of a semi-regular hexagon on the triangular lattice. In this paper we generalize MacMahon's classical theorem by q-enumerating lozenge tilings of a new family of hexagons with four adjacent triangles removed from their boundary.

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