Proof of two conjectures of Ciucu and Krattenthaler on the enumeration of lozenge tilings of hexagons with cut off corners

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:133

Article

Ciucu, Mihai¹  Fischer, Ilse² 

[1] Indiana Univ, Dept Math, Bloomington, IN 47401 USA

[2] Univ Vienna, Fak Math, A-1090 Vienna, Austria

关键词: Lozenge tilings;    Kuo's condensation;    Tiling enumeration;    Perfect matchings;    Plane partitions;   

DOI  :  10.1016/j.jcta.2015.02.008

来源: Elsevier

【 摘 要 】

In their 2002 paper, Ciucu and Krattenthaler proved several product formulas for the number of lozenge tilings of various regions obtained from a centrally symmetric hexagon on the triangular lattice by removing maximal staircase regions from two non-adjacent corners. For the case when the staircases are removed from adjacent corners of the hexagon, they presented two conjectural formulas, whose proofs, as they remarked, seemed at the time a formidable task. In this paper we prove those two conjectures. Our proofs proceed by first generalizing the conjectures, and then proving them by induction using Kuo's graphical condensation method. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free