Frankl's Conjecture Is True for Lower Semimodular Lattices

@article{Reinhold2000FranklsCI,
  title={Frankl's Conjecture Is True for Lower Semimodular Lattices},
  author={J. Reinhold},
  journal={Graphs and Combinatorics},
  year={2000},
  volume={16},
  pages={115-116}
}
  • J. Reinhold
  • Published 2000
  • Mathematics, Computer Science
  • Graphs and Combinatorics
Abstract. It is shown that every finite lower semimodular lattice L with |L|≥2 contains a join-irreducible element x such that at most |L|/2 elements y∈L satisfy y≥x. 

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References

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Frankl's Conjecture is True for Modular Lattices
Abstract. It is shown that every finite modular lattice L with |L|≥2 contains a join-irreducible element x∈L such that at most |L|/2 elements y∈L satisfy y≥x.