Author

Xiao-Chen Zhao

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Preprint Sep 2026

The maximum $t$-diversity of $t$-intersecting families of permutations

The study of $t$-intersecting families in symmetric groups received lots of attention in the last two decades. In this paper, we study two different kinds of stability results for $t$-intersecting families in symmetric groups. Let $\Sigma_n$ denote the symmetric group on $\{1,2,\ldots,n\}$. The $t$-diversity $\gamma_t(...

Yu-Hang Cao, Gen-Nian Ge, Jian Wang et al. · 0 citations

Preprint Jul 2026

Largest Sperner families with restricted differences

Let $L$ be a fixed set of positive integers. A family $\mathcal{F}\subseteq 2^{[n]}$ is called $L$-differencing if $\lvert A\setminus B\rvert\in L$ for every ordered pair of distinct members $A,B\in\mathcal{F}$. A longstanding conjecture of Frankl, proposed in 1985, asserts that every $L$-differencing family has size a...

Gen-Nian Ge, Zixiang Xu, Xiao-Chen Zhao · 0 citations