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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On symmetric 3-wise intersecting families
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by David Ellis and Bhargav Narayanan PDF
Proc. Amer. Math. Soc. 145 (2017), 2843-2847 Request permission

Abstract:

A family of sets is said to be symmetric if its automorphism group is transitive, and $3$-wise intersecting if any three sets in the family have nonempty intersection. Frankl conjectured in 1981 that if $\mathcal {A}$ is a symmetric $3$-wise intersecting family of subsets of $\{1,2,\dots ,n\}$, then $|\mathcal {A}| = o(2^n)$. Here, we give a short proof of Frankl’s conjecture using a ‘sharp threshold’ result of Friedgut and Kalai.
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Additional Information
  • David Ellis
  • Affiliation: School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, United Kingdom
  • Email: d.ellis@qmul.ac.uk
  • Bhargav Narayanan
  • Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
  • MR Author ID: 1058391
  • Email: b.p.narayanan@dpmms.cam.ac.uk
  • Received by editor(s): August 18, 2016
  • Published electronically: January 23, 2017
  • Communicated by: Patricia L. Hersh
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 2843-2847
  • MSC (2010): Primary 05D05; Secondary 05E18
  • DOI: https://doi.org/10.1090/proc/13452
  • MathSciNet review: 3637934