Diversity
Combinatorics
2018-11-06 v1 Discrete Mathematics
Abstract
Given a family , its diversity is the number of sets not containing an element with the highest degree. The concept of diversity has proven to be very useful in the context of -uniform intersecting families. In this paper, we study (different notions of) diversity in the context of other extremal set theory problems. One of the main results of the paper is a sharp stability result for cross-intersecting families in terms of diversity and, slightly more generally, sharp stability for the Kruskal--Katona theorem.
Cite
@article{arxiv.1811.01111,
title = {Diversity},
author = {Peter Frankl and Andrey Kupavskii},
journal= {arXiv preprint arXiv:1811.01111},
year = {2018}
}