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Research Article Open Access

Proof of Frankl's Conjecture: A Non-Constructive Approach

Yonghong Liu1
  • 1 School of Automation, Wuhan University of Technology, China

Abstract

Let U be a finite set and X  a family of nonempty subsets of U,which is closed under unions. We establish a connection between Frankl'sconjecture and equipollence sets, in which a complementary set is anEquipollence set on the Frobenius group. We complete the proof of theunion-closed sets using a non-constructive approach. The proof relies upon thatwe need to prove, that the series of the prime divisor diverges, and thereexists xi which appears at least half distributedin subsets.

Journal of Mathematics and Statistics
Volume 18 No. 1, 2022, 134-137

DOI: https://doi.org/10.3844/jmssp.2022.134.137

Submitted On: 7 May 2022 Published On: 21 September 2022

How to Cite: Liu, Y. (2022). Proof of Frankl's Conjecture: A Non-Constructive Approach. Journal of Mathematics and Statistics, 18(1), 134-137. https://doi.org/10.3844/jmssp.2022.134.137

Open AccessCopyright: © 2022 Yonghong Liu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Frankl’s Conjecture
  • Union-Closed
  • Extremal Set Theory
  • Complementary Sets
  • Primes