Author

Yuhao Zhao

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Preprint Aug 2026

A superlogarithmic saving for Oddtown modulo composite numbers

Let $f_{\ell}(n)$ be the largest size of a family $\mathcal{A}\subseteq2^{[n]}$ such that no member has size divisible by $\ell$, while the intersection of every two distinct members has size divisible by $\ell$, and let $\omega(\ell)$ denote the number of distinct prime divisors of $\ell$. For any prime power $\ell$,...

Yuhao Zhao · 0 citations

Preprint Jul 2026

Lower bounds on the strength of the determinant

We establish new lower bounds for the strength and partition rank of the determinant. For every prime $p$, we prove the exact identity \[ \operatorname{str}(\mathrm{det}_p)=p. \] A weak monotonicity argument, combined with a bound for gaps between consecutive primes, then gives $\operatorname{str}(\mathrm{det}_n)\ge (1...

Qiyuan Chen, Yuhao Zhao · 0 citations