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Union-closed sets and Horn Boolean functions
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Lozin, Vadim V. and Zamaraev, Viktor (2024) Union-closed sets and Horn Boolean functions. Journal of Combinatorial Theory, Series A, 202 . 105818. doi:10.1016/j.jcta.2023.105818 ISSN 0097-3165.
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Official URL: http://doi.org/10.1016/j.jcta.2023.105818
Abstract
A family of sets is union-closed if the union of any two sets from belongs to. The union-closed sets conjecture states that if is a finite union-closed family of finite sets, then there is an element that belongs to at least half of the sets in. The conjecture has several equivalent formulations in terms of other combinatorial structures such as lattices and graphs. In its whole generality the conjecture remains wide open, but it was verified for various important classes of lattices, such as lower semimodular lattices, and graphs, such as chordal bipartite graphs. In the present paper we develop a Boolean approach to the conjecture and verify it for several classes of Boolean functions, such as submodular functions and double Horn functions.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Algebraic functions, Algebra, Boolean, Set theory, Mathematical analysis | ||||||||
Journal or Publication Title: | Journal of Combinatorial Theory, Series A | ||||||||
Publisher: | Elsevier BV | ||||||||
ISSN: | 0097-3165 | ||||||||
Official Date: | February 2024 | ||||||||
Dates: |
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Volume: | 202 | ||||||||
Article Number: | 105818 | ||||||||
DOI: | 10.1016/j.jcta.2023.105818 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 3 November 2023 | ||||||||
Date of first compliant Open Access: | 7 November 2023 |
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