The profile polytope of non-trivial intersecting families

Dániel Gerbner

The profile polytope of non-trivial intersecting families

Combinatorics 2022-03-11 v2

Authors: Dániel Gerbner

Abstract

The profile vector of a family $\mathcal{F}$ of subsets of an $n$ -element set is $(f_0,f_1, \ldots, f_n)$ where $f_i$ denotes the number of the $i$ -element members of $\mathcal{F}$ . In this paper we determine the extreme points of the set of profile vectors for the class of non-trivial intersecting families.

Keywords

intersecting families profile vector profile polytope extreme points combinatorics

Cite

@article{arxiv.2109.05615,
  title  = {The profile polytope of non-trivial intersecting families},
  author = {Dániel Gerbner},
  journal= {arXiv preprint arXiv:2109.05615},
  year   = {2022}
}

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