发表机构
Department of Mathematical Sciences, Tsinghua University（清华大学数学科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究 $t$-wise $L$-相交 $r$-团的最大数目，证明非等差情形下为 $o(n^{|L|})$，等差情形下给出渐近公式，推广了 Helliar 和 Liu 的结果。
AI 中文摘要
设 $r,t\ge 3$ 为整数，$L=\{\ell_1,\ell_2,\ldots,\ell_s\}\subseteq [0,r-1]$ 为固定整数集合，满足 $|L|\neq r$ 且 $\ell_1<\ell_2<\cdots<\ell_s$。对每个整数 $n$，令 $\Psi_{r}(n,L,t)$ 为 $n$ 顶点图中 $r$-团的最大数目，其中这些 $r$-团作为顶点集的 $r$-子集族，构成 $t$-wise $L$-相交族。本文证明：当序列 $\ell_1,\ell_2,\ldots,\ell_s,r$ 不构成等差数列时，$\Psi_{r}(n,L,t)=o(n^{|L|})$；当该序列构成等差数列时，我们给出 $\Psi_{r}(n,L,t)$ 的渐近公式。当 $t=2$ 时，我们的结果恰好是 Helliar 和 Liu 的结果。
英文摘要
Let $r,t\ge 3$ be integers and $L=\{\ell_1,\ell_2,\ldots,\ell_s\}\subseteq [0,r-1]$ a fixed set of integers with $|L|\neq r$ and $\ell_1<\ell_2<\cdots<\ell_s$. For each integer $n$, let $Ψ_{r}(n,L,t)$ be the maximum number of $r$-cliques in an $n$-vertex graph whose $r$-cliques, viewed as a family of $r$-subsets of the vertex set, form a $t$-wise $L$-intersecting family. In this paper, we prove that $Ψ_{r}(n,L,t)=o(n^{|L|})$ when the sequence $\ell_1,\ell_2,\ldots,\ell_s,r$ does not form an arithmetic progression, and we give an asymptotic formula for $Ψ_{r}(n,L,t)$ when this sequence does form an arithmetic progression. When $t=2$, our results are exactly Helliar and Liu's results.
