ARTICLE
TITLE

Lower bound on the number of meet-irreducible elements in extremal lattices

SUMMARY

Extremal lattices are lattices maximal in size with respect to the number n of their join-irreducible elements with bounded Vapnik-Chervonekis dimension k. It is natural, however, to estimate the size of a lattice also with respect to the number of its meet-irreducible elements. Although this number may differ for nonequivalent (n, k + 1)-extremal lattices, we show that each (n, k + 1)-extremal lattice has k disjoint chains of meet-irreducible elements, each of length n - k + 2.

PAGES
pp. 26 - 48
COLLECTIONS
Mathematics

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