Tiling with arbitrary tiles
Vytautas Gruslys, Imre Leader, Ta Sheng Tan

TL;DR
The paper proves that any finite tile in integer lattice space can tile some higher-dimensional integer lattice, resolving a conjecture and advancing understanding of tiling problems in discrete geometry.
Contribution
It establishes that every finite tile in al^n can tile al^d for some d, confirming Chalcraft's conjecture.
Findings
Any finite tile in al^n can tile al^d for some d
Resolution of Chalcraft's conjecture in tiling theory
Advances understanding of tiling possibilities in higher dimensions
Abstract
Let be a tile in , meaning a finite subset of . It may or may not tile , in the sense of having a partition into copies of . However, we prove that does tile for some . This resolves a conjecture of Chalcraft.
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Taxonomy
TopicsCellular Automata and Applications · DNA and Biological Computing · Quasicrystal Structures and Properties
