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http://dx.doi.org/10.4134/BKMS.b190301

ON DIVERSITY OF CERTAIN t-INTERSECTING FAMILIES  

Ku, Cheng Yeaw (Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University)
Wong, Kok Bin (Institute of Mathematical Sciences University of Malaya)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 815-829 More about this Journal
Abstract
Let [n] = {1, 2, …, n} and 2[n] be the set of all subsets of [n]. For a family 𝓕 ⊆ 2[n], its diversity, denoted by div(𝓕), is defined to be $$div(\mathcal{F})=\min_{x{\in}[n]}\{{\mid}{\mathcal{F}}(\bar{x}){\mid}\}$$, where ${\mathcal{F}}(\bar{x})=\{F{\in}{\mathcal{F}}:x{\not\in}F\}$. Basically, div(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; $Erd{\ddot{o}}s$-Ko-Rado; divers;
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