For a family $\mathcal F\subseteq\binom{[n]}k$ and $R\in\binom{[n]}r$, let $d_{\mathcal F}(R)=|\{F\in\mathcal F:R\subseteq F\}|$ and $\ell_{r,p}(\mathcal F)=\sum_{R\in\binom{[n]}r}d_{\mathcal F}(R)^p$; write $co_p(\mathcal F)=\ell_{k-1,p}(\mathcal F)$ for the codegree power sum. We introduce a method that uses convexit...
Meng-Yue Cao, Mei Lu, Hai-Xiang Zhang· 1 citation· ⚡1
The spectral Erd\H{o}s--Ko--Rado problem asks for the largest adjacency-tensor spectral radius of a $t$-intersecting $k$-uniform family. Keevash, Lenz and Mubayi proved that, for fixed $k,t$ and sufficiently large $n$, the unique extremal family is a full $t$-star, and asked whether such a theorem extends to all $n$. L...
Meng-Yue Cao, Mei Lu, Hai-Xiang Zhang· 0 citations
For a family $\mathcal{F}\subseteq\binom{[n]}k$ and $R\in\binom{[n]}r$, let $d_{\mathcal{F}}(R)=|\{F\in\mathcal{F}:R\subseteq F\}|$ and $\ell_{r,p}(\mathcal{F})=\sum_{R\in\binom{[n]}r}d_{\mathcal{F}}(R)^p$; at the codegree level, write $co_p(\mathcal{F})=\ell_{k-1,p}(\mathcal{F})$. We introduce a new convex-transferenc...
Mengyue Cao, Mei Lu, Haixiang Zhang· 1 citation· ⚡1
Let $V$ be an $n$-dimensional vector space over the finite field $\mathbb F_q$, and let $\mathcal F\subsetneq\genfrac{[}{]}{0pt}{}{V}{k}$. The \emph{projective Ore-degree} of $\mathcal F$ is the minimum, over all $k$-subspaces $S\notin\mathcal F$, of the sum of the $\mathcal F$-degrees of the projective points containe...
Meng-Yue Cao, Mei Lu, Xuyang Yan et al.· 0 citations
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