Plane partitions of shifted double staircase shape

[摘要] We give a product formula for the number of shifted plane partitions of shifted double staircase shape with bounded entries. This is the first new example of a family of shapes with a plane partition product formula in many years. The proof is based on the theory of lozenge tilings; specifically, we apply the free boundary Kuo condensation due to Ciucu. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-01

[关键词] Plane partition;Lozenge tiling;Dimer;Product formula;Order polynomial;Kuo condensation