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

  • B. O. Chornomaz Харківський національний університет ім.В.Н.Каразіна
Keywords: Extremal lattices; Vapnik-Chervonekis dimension; meet-irreducible elements

Abstract

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.

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References

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Published
2017-11-29
Cited
How to Cite
Chornomaz, B. O. (2017). Lower bound on the number of meet-irreducible elements in extremal lattices. Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, 86, 26-48. https://doi.org/10.26565/2221-5646-2017-86-04
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