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On diversity of certain t-intersecting families

Cheng Yeaw Ku|Kok Bin Wong
대한수학회 (The Korean Mathematical Society)|2020.07|대한수학회보 (Bulletin of the KMS)|제57권 제4호|pp. 815-829|DOI 10.4134/BKMS.b190301

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참고문헌

키워드

diversity$t$-intersecting familyErd{\H o}s-Ko-Rado
주제분류수학

초록

Let $[n]=\{1,2,\dots, n\}$ and $2^{[n]}$ be the set of all subsets of $[n]$. For a family $\F\subseteq 2^{[n]}$, its diversity, denoted by $\di(\F)$, is defined to be \begin{align*} \di(\F)=\min_{x\in [n]} \left\{ \left\vert \F(\overline x) \right\vert \right\}, \end{align*} where $\F(\overline x)=\left\{ F\in\F : x\notin F \right\}$. Basically, $\di(\F)$ measures how far $\F$ is from a trivial intersecting family, which is called a star. In this paper, we consider a generalization of diversity for $t$-intersecting family.

Abstract

Let $[n]=\{1,2,\dots, n\}$ and $2^{[n]}$ be the set of all subsets of $[n]$. For a family $\F\subseteq 2^{[n]}$, its diversity, denoted by $\di(\F)$, is defined to be \begin{align*} \di(\F)=\min_{x\in [n]} \left\{ \left\vert \F(\overline x) \right\vert \right\}, \end{align*} where $\F(\overline x)=\left\{ F\in\F : x\notin F \right\}$. Basically, $\di(\F)$ measures how far $\F$ is from a trivial intersecting family, which is called a star. In this paper, we consider a generalization of diversity for $t$-intersecting family.

참고문헌 (36)

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