Forced perimeter in Elnitksy polygons

preprint2020arXivOpen access

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.

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