Mathematics > Combinatorics
arXiv:2606.26191 (math)
[Submitted on 24 Jun 2026]
Abstract:For a set of $m$ subsets of a universe set of size $n$, we construct a Boolean polynomial $\mathrm{ICC}_{m,n}(X)$ such that the Union-Closed Conjecture is true for this $m$ and $n$ if and only if $\mathrm{ICC}_{m,n}(X)$ is the zero Boolean polynomial. We use an equivalent formulation, called the Intersection-Closed Conjecture.
Submission history
From: Mario DeFranco [view email]
[v1]
Wed, 24 Jun 2026 14:14:35 UTC (5 KB)
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