Proof of Blum's conjecture on hexagonal dungeons

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:125

Article

Ciucu, Mihai¹  Lai, Tri¹ 

[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

关键词: Tilings;    Perfect matchings;    Dual graph;    Graphical condensation;    Aztec dungeons;    Hexagonal dungeons;   

DOI  :  10.1016/j.jcta.2014.03.008

来源: Elsevier

【 摘 要 】

Matt Blum conjectured that the number of tilings of the hexagonal dungeon of sides a, 2a, b, a, 2a, b (where b >= 2a) is 13(2a2)14[a(2)/2] (Propp, 1999 [4]). In this paper we present a proof for this conjecture using Kuo's Graphical Condensation Theorem (Kuo, 2004 [2]). (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free