A pentagonal number theorem for tribone tilings

2022/06/09 by Kim, Jesse, Propp, James · 1 citation
Computer Science · Engineering · Materials Science · #05B50 #52C20 #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Quasicrystal Structures and Properties #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2206.04223

openalex publication_date 2022/06/09 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

Abstract

Conway and Lagarias showed that certain roughly triangular regions in the hexagonal grid cannot be tiled by shapes Thurston later dubbed tribones. Here we study a two-parameter family of roughly hexagonal regions in the hexagonal grid and show that a tiling by tribones exists if and only if the two parameters associated with the region are the paired pentagonal numbers k(3k ± 1)/2.

Cited by

• Stones, Bones, and Snakes: Tilability of the hexagonal grid via the double dimer model

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