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A proof of Frankl’s union-closed sets conjecture for dismantlable lattices

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Abstract

In this paper, we prove Frankl’s Union-Closed Sets Conjecture for the class of dismantlable lattices, a more general class than the class of planar lattices. As a consequence of this result, we also prove that an upper semimodular lattice with breadth at most two satisfies the Conjecture.

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Authors and Affiliations

  1. Department of Mathematics, Savitribai Phule Pune University, Pune, 411007, India

    Vinayak Joshi & B. N. Waphare

  2. Department of Mathematics, College of Engineering, Pune, 411005, India

    S. P. Kavishwar

Authors
  1. Vinayak Joshi
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  2. B. N. Waphare
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  3. S. P. Kavishwar
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Correspondence to Vinayak Joshi.

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Presented by R. Quackenbush.

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Joshi, V., Waphare, B.N. & Kavishwar, S.P. A proof of Frankl’s union-closed sets conjecture for dismantlable lattices. Algebra Univers. 76, 351–354 (2016). https://doi.org/10.1007/s00012-016-0405-0

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  • DOI: https://doi.org/10.1007/s00012-016-0405-0

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