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A Note on the Union-closed Sets Conjecture

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arxiv 2309.01704 v3 pith:ET76GH2B submitted 2023-09-04 math.CO

classification math.CO
keywords rowsclosedcolumnsconjectureexistencematrixtextitunder
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abstract

Let $M$ be a non-zero binary matrix with distinct rows where the rows are closed under certain logical operators. In this article, we investigate the existence of columns containing an equal or greater number of ones than zeros. Specifically, the existence of such columns when the rows of the matrix are closed under $\textit{material conditional}$ leads us to a weaker version of the $\textit{Union-Closed Set Conjecture}$.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the Averaging Problem of Ideal Families Related to Frankl's Conjecture with Formal Proof by Lean 4

    math.CO 2025-04 conditional novelty 5.0 of 10

    Every ideal family of sets is average rare: the average vertex degree is at most half the number of hyperedges, with a formal Lean 4 proof.

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