Intersecting families of sets and permutations: a survey

Details Intersecting families of sets and permutations: a survey Intersecting families of sets and permutations: a survey

2011-06-30

arxiv.org/abs/1106.6144v1

Mathematics

Combinatorics

21 pages

Scientific paper

A family $\mathcal{A}$ of sets is said to be \emph{$t$-intersecting} if any two sets in $\mathcal{A}$ have at least $t$ common elements. A central problem in extremal set theory is to determine the size or structure of a largest $t$-intersecting sub-family of a given family $\mathcal{F}$. We give a survey of known results, conjectures and open problems for various important families $\mathcal{F}$, namely, power sets, levels of power sets, hereditary families, families of signed sets, families of labeled sets, and families of permutations. We also provide some extensions and consequences of known results.

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