Intersecting Families of Finite Sets and Fixed-point-Free 2-Elements

P. J. Cameron; P. Frankl; W. M. Kantor

doi:10.1016/S0195-6698(89)80042-3

Intersecting Families of Finite Sets and Fixed-point-Free 2-Elements

P. J. Cameron^*, P. Frankl, W. M. Kantor

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We study the maximum cardinality of a pairwise-intersecting family of subsets of an n-set, or the size of the smallest set in such a family, under either of the assumptions that it is regular (as a hypergraph) or that it admits a transitive permutation group. Not surprisingly, results under the second assumption are stronger. We also give some results for 4-wise intersecting families under the same assumptions.

Original language	English
Pages (from-to)	149-160
Number of pages	12
Journal	European Journal of Combinatorics
Volume	10
Issue number	2
DOIs	https://doi.org/10.1016/S0195-6698(89)80042-3
Publication status	Published - 1 Jan 1989

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title = "Intersecting Families of Finite Sets and Fixed-point-Free 2-Elements",

abstract = "We study the maximum cardinality of a pairwise-intersecting family of subsets of an n-set, or the size of the smallest set in such a family, under either of the assumptions that it is regular (as a hypergraph) or that it admits a transitive permutation group. Not surprisingly, results under the second assumption are stronger. We also give some results for 4-wise intersecting families under the same assumptions.",

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AB - We study the maximum cardinality of a pairwise-intersecting family of subsets of an n-set, or the size of the smallest set in such a family, under either of the assumptions that it is regular (as a hypergraph) or that it admits a transitive permutation group. Not surprisingly, results under the second assumption are stronger. We also give some results for 4-wise intersecting families under the same assumptions.

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Intersecting Families of Finite Sets and Fixed-point-Free 2-Elements

Abstract

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