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math.CO2026
Periodic Tilings of Cardinality Twice a Prime or Nine in Arbitrary Dimension
Hu Tan, Ying Zhang
We prove that every finite translational tile of of cardinality , where is an odd prime, or of cardinality nine admits a fully periodic tiling complement. The…
math.CO2026
Fuglede's Conjecture for Cyclic Groups of Square-free Order
Hu Tan, Ying Zhang
We prove Fuglede's conjecture for finite cyclic groups of square-free order. Specifically, if \(N\) is square-free and \(A\subseteq \mathbb Z_N\) is nonempty with \(|A|=m\), then \…