2 papers
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.NT2026
A Proof of Fraenkel's Conjecture
Hu Tan, Ying Zhang
Fraenkel's conjecture asserts that a partition of the integers into at least three Beatty sequences with distinct moduli has the binary densities , normalized…