Forced perimeter in Elnitksy polygons

Authors :: Tenner, Bridget Eileen
Publication Year :: 2020
Abstract: We study tiling-based perimeter and characterize when a given perimeter tile appears in all rhombic tilings of an Elnitsky polygon. Regardless of where on the perimeter this tile appears, its forcing can be described in terms of 321-patterns. We characterize the permutations with maximally many forced right-perimeter tiles, and show that they are enumerated by the Catalan numbers.<br />Comment: 10 pages