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On the widths of finite distributive lattices

✍ Scribed by Jeff Kahn; Michael Saks

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 707 KB
Volume: 63
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90007-0

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✦ Synopsis

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 2 is a finite distributive lattice whose width w(Z) (size of the largest antichain) is at least n(R), then IZ/a Rw(Z). In words this says that as one considers ~ increasingly large distributive lattices, the maximum sized antichain contains small proportion of the elements.

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