Author

Chong Shangguan

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Preprint Sep 2026

Thresholds and spread in set systems of bounded VC-dimension

Let $p_c(\mathcal F)$, $q(\mathcal F)$, and $q_f(\mathcal F)$ denote the threshold, expectation threshold, and fractional expectation threshold of a family $\mathcal F$ of nonempty subsets of a finite set, respectively. We prove that there is an absolute constant $C>0$ such that, if $\mathcal F$ has VC dimension at mos...

Chong Shangguan · 0 citations

Preprint Aug 2026

The Optimal Asymptotic Rate of Generalized Covering Codes

Let $G_q$ be an alphabet of size $q\geq2$. We determine the optimal asymptotic rate of generalized covering codes $C\subseteq G_q^n$, whose covering centers in $G_q^{t\times n}$ are constrained to the product form $C^t$. For every fixed integer $t\geq1$ and every $\rho\in[0,1]$, we prove that \[ \kappa_t(\rho,q)= \begi...

Heng Li, Chong Shangguan, Heng-Jia Wei · 3 citations