Author

Hui-Yue Tan

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Preprint Sep 2026

Sharp Diameter Bounds for Nonnegative Cyclotomic Multiples

Let $N\ge2$ and let $p$ be its least prime divisor. We prove that every nonzero polynomial with nonnegative real coefficients divisible by $\Phi_N$ has support diameter at least $(p-1)N/p$. Equality holds precisely for positive scalar multiples of monomial shifts of the $p$-term geometric sum \(\sum_{j=0}^{p-...

Hui-Yue Tan, Ying Zhang · 0 citations

Preprint Sep 2026

A Proof of Fraenkel's Conjecture

Fraenkel's conjecture asserts that a partition of the integers into at least three Beatty sequences with distinct moduli has the binary densities $1,2,4,\ldots,2^{m-1}$, normalized by $2^m-1$. We prove the conjecture through a dimension-free intermediate statement: every such partition contains a component of density a...

Hui-Yue Tan, Ying Zhang · 0 citations