Enumeration of lozenge tilings of a hexagon with a maximal staircase and a unit triangle removed

Abstract

Proctor proved a formula for the number of lozenge tilings of a hexagon with side-lengths $a,b,c,a,b,c$ after removing a "maximal staircase." Ciucu then presented a weighted version of Proctor's result. Here we present weighted and unweighted formulas for a similar region which has an additional unit triangle removed. We use Kuo's graphical condensation method to prove the results. By applying the factorization theorem of Ciucu, we obtain a formula for the number of lozenge tilings of a hexagon with three holes on consecutive edges.

12 pages, 9 figures. arXiv admin note: text overlap with arXiv:1510.04486

References in corpus (1)

• A $q$-enumeration of lozenge tilings of a hexagon with three dents