OpenAlex ·
Entropy bounds and global couplings for union-closed families
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.08291
- Original
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- Topics
Abstract
We give a computer-assisted proof that every finite union-closed family containing a nonempty set has an element in at least 0.38288525 of its members. The argument combines independent sampling with conditionally independent sampling and an explicit product lower bound for a binary-entropy kernel. We identify the limiting constant of this pointwise method through a one-variable stationary equation. We also construct a global coupling by balancing inverse union multiplicities and prove a strictly positive, quantitative entropy gain over independent sampling. Combining the two arguments gives an additional frequency bound depending on the size of the family.
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