The number of tiles of ℤ^d

2023/03/14 by Itaï Benjamini, Gady Kozma, Benjamini, Itai +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Cellular Automata and Applications #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2303.07956

openalex publication_date 2023/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that the number of subsets of [n]^d that tile ℤ^d is (3^(1)/(3))^{nd ± o(nd)}.

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