Three product formulas for ratios of tiling counts of hexagons with\n collinear holes

2019/06/11 by Seok Hyun Byun, Byun, Seok Hyun
Materials Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1906.04532

openalex publication_date 2019/06/11 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Rosengren found an explicit formula for a certain weighted enumeration of\nlozenge tilings of a hexagon with an arbitrary triangular hole. He pointed out\nthat a certain ratio corresponding to two such regions has a nice product\nformula. In this paper, we generalize this to hexagons with arbitrary collinear\nholes. It turns out that, by using same approach, we can also generalize\nCiucu's work on the number and the number of centrally symmetric tilings of a\nhexagon with a fern removed from its center. This proves a recent conjecture of\nCiucu.\n

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