Proof of a refinement of Blum's conjecture on hexagonal dungeons
Abstract
Matt Blum conjectured that the number of tilings of a hexagonal dungeon with side-lengths a,2a,b,a,2a,b (for b≥2a) equals 132a214 a2/2. Ciucu and the author of the present paper proved the conjecture by using Kuo's graphical condensation method. In this paper, we investigate a 3-parameter refinement of the conjecture and its application to enumeration of tilings of several new types of the hexagonal dungeons.
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