On regular 3-wise intersecting families

Keith Frankston, Jeff Kahn, Bhargav Narayanan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Ellis and the third author showed, verifying a conjecture of Frankl, that any 3-wise intersecting family of subsets of {1, 2,…,n} admitting a transitive automorphism group has cardinality o(2n), while a construction of Frankl demonstrates that the same conclusion need not hold under the weaker constraint of being regular. Answering a question of Cameron, Frankl, and Kantor from 1989, we show that the restriction of admitting a transitive automorphism group may be relaxed significantly: we prove that any 3-wise intersecting family of subsets of {1, 2,…,n} that is regular and increasing has cardinality o(2n).

Original languageEnglish (US)
Pages (from-to)4091-4097
Number of pages7
JournalProceedings of the American Mathematical Society
Volume146
Issue number10
DOIs
StatePublished - 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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