Wildest SL₂-tilings

2025/08/13 by Zabolotskii, Andrei
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.09773

Abstract

Tame SL₂-tilings are related to Farey graph and friezes; much less is known about wild (not tame) SL₂-tilings. In this note, we demonstrate SL₂-tilings that are maximally wild: we prove that the maximum wild density of an integer SL₂-tiling is \tfrac25 and present SL₂-tilings over ℤ/Nℤ with wild density 1.

Citations

• On wild frieze patterns

Related

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• 3D Farey graph, lambda lengths and SL₂-tilings
• SL_k-Tilings and Paths in ℤ^k
• SL₂-Tilings Do Not Exist in Higher Dimensions (mostly)
• On wild frieze patterns