On the widths of finite distributive lattices

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Abstract

The following conjecture of U Faigle and B Sands is proved: For every number R > 0 there exists a number n(R) such that if L is a finite distributive lattice whose width w(L) (size of the largest antichain) is at least n(R), then |L| ≥ Rw(L). In words this says that as one considers increasingly large distributive lattices, the maximum sized antichain contains a vanishingly small proportion of the elements.

Original languageEnglish (US)
Pages (from-to)183-195
Number of pages13
JournalDiscrete Mathematics
Volume63
Issue number2-3
DOIs
StatePublished - 1987

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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