On diversity of certain $t$-intersecting families
Bull. Korean Math. Soc. 2020 Vol. 57, No. 4, 815-829
https://doi.org/10.4134/BKMS.b190301
Published online July 8, 2020
Printed July 31, 2020
Cheng Yeaw Ku, Kok Bin Wong
Nanyang Technological University; University of Malaya
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.
Keywords : $t$-intersecting family, Erd{\H o}s-Ko-Rado, diversity
MSC numbers : 05C05, 05D99
Supported by : This project is partially supported by the Fundamental Research Grant Scheme (FRGS) FRGS/1/2019/STG06/UM/02/10
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