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arXiv · 1511.00170

Union-Free Families of Subsets

Andy Loo
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Abstract

This paper discusses the question of how many non-empty subsets of the set $[n] = \{ 1, 2, ..., n\}$ we can choose so that no chosen subset is the union of some other chosen subsets. Let $M(n)$ be the maximum number of subsets we can choose. We construct a series of such families, which leads to lower bounds on $M(n)$. We also give upper bounds on $M(n)$. Finally, we propose several conjectures on the tightness of our lower bound for $M(n)$.

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BibTeXRIS

Andy Loo. 2015-10-31. Union-Free Families of Subsets. https://arxiv.org/abs/1511.00170

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