Bulletin of the Korean Mathematical Society (대한수학회보)

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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)
  • Received : 2019.03.18
  • Accepted : 2020.01.31
  • Published : 2020.07.31
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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

Acknowledgement

We would like to thank the anonymous referee for the comments and suggestions that have improved the organization of this paper. This project is partially supported by the Fundamental Research Grant Scheme (FRGS) FRGS/1/2019/STG06/UM/02/10.

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