Tilings of hexagons with a removed triad of bowties

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:178

Article

Ciucu, Mihai¹  Tri Lai²  Rohatgi, Ranjan³ 

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

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

[3] St Marys Coll, Dept Math & Comp Sci, Notre Dame, IN 46556 USA

关键词: Lozenge tilings;    Plane partitions;    Graphical condensation;    Product formulas;    Exact enumeration;   

DOI  :  10.1016/j.jcta.2020.105359

来源: Elsevier

【 摘 要 】

In this paper we consider arbitrary hexagons on the triangular lattice with three arbitrary bowtie-shaped holes, whose centers form an equilateral triangle. The number of lozenge tilings of such general regions is not expected - and indeed is not - given by a simple product formula. However, when considering a certain natural normalized counterpart (R) over bar of any such region R, we prove that the ratio between the number of tilings of R and the number of tilings of (R) over bar is given by a simple, conceptual product formula. Several seemingly unrelated previous results from the literature - including Lai's formula for hexagons with three dents and Ciucu and Krattenthaler's formula for hexagons with a removed shamrock - follow as immediate special cases of our result. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free