On diversity of certain T-intersecting families

• Main Authors: Ku, Cheng Yeaw, Wong, Kok Bin
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2021
• Subjects: Engineering::Mathematics and analysis; T-intersecting Family; Erd ̋os-Ko-Rado
• Online Access: https://hdl.handle.net/10356/147616
• Institution: Nanyang Technological University

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(F) = minx∈[n]{|F(x)|}, where F(x) = {F ϵ F: x ⊄ F }. Basically, div(F) measures how far F is from a trivial intersecting family, which is called a star. In...