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A class of lattices and Boolean functions related to the Manickam-Miklös-Singhi conjecture. (English) Zbl 1259.05178

Summary: The aim of this paper is to build a new family of lattices related to some combinatorial extremal sum problems, in particular to a conjecture of N. Manickam and D. Miklós [Colloq. Math. Soc. János Bolyai 52, 385–392 (1988; Zbl 0726.11014)] and N. Manickam and N. M. Singhi [J. Comb. Theory, Ser. A 46, No. 1, 91–103 (1988; Zbl 0645.05023)]. We study the fundamental properties of such lattices and of a particular class of boolean functions defined on them.

MSC:

05D05 Extremal set theory
11B75 Other combinatorial number theory
05A05 Permutations, words, matrices
06B99 Lattices
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