Cyclically Symmetric Lozenge Tilings of a Hexagon with Four Holes

2017/05/02 by Tri Lai, Lai, Tri, Ranjan Rohatgi +1
Engineering · Materials Science · Mathematics · #05A15 #05B45 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Quasicrystal Structures and Properties #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1705.01122

openalex publication_date 2017/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The work of Mills, Robbins, and Rumsey on cyclically symmetric plane partitions yields a simple product formula for the number of lozenge tilings of a regular hexagon, which are invariant under roation by 120^∘. In this paper we generalize this result by enumerating the cyclically symmetric lozenge tilings of a hexagon in which four triangles have been removed in the center.

Citations

• Plane partitions I: a generalization of MacMahon's formula

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