Lozenge tilings of doubly-intruded hexagons

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:167

Article

Ciucu, Mihai¹  Lai, Tri² 

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

[2] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

关键词: Perfect matchings;    Lozenge tilings;    Dual graph;    Kuo condensation;    Plane partitions;   

DOI  :  10.1016/j.jcta.2019.05.004

来源: Elsevier

【 摘 要 】

Motivated in part by Propp's intruded Aztec diamond regions, we consider hexagonal regions out of which two horizontal chains of triangular holes (called ferns) are removed, so that the chains are at the same height, and are attached to the boundary. By contrast with the intruded Aztec diamonds (whose numbers of domino tilings contain some large prime factors in their factorization), the number of lozenge tilings of our doubly-intruded hexagons turns out to be given by simple product formulas in which all factors are linear in the parameters. We present in fact q-versions of these formulas, which enumerate the corresponding plane partitions-like structures by their volume. We also pose some natural statistical mechanics questions suggested by our setup, which should be possible to tackle using our formulas. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free