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Better bounds for the union-closed sets conjecture using the entropy approach

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arxiv 2212.12500 v2 pith:BGXKLCWF submitted 2022-12-23 math.CO

Better bounds for the union-closed sets conjecture using the entropy approach

classification math.CO
keywords approachentropyconjectureknownunion-closedbehindbestbetter
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abstract

We improve the best known constant $\frac{3-\sqrt 5}{2}$ for which the union-closed conjecture is known to be true, by using dependent samples as suggested by Sawin and the entropy approach on this problem initiated by Gilmer. Meanwhile, we focus on the intuition behind this entropy approach and its boundaries.

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Cited by 2 Pith papers

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

  1. Redundancy Is All You Need (for CSP Sparsification)

    cs.DS 2024-11 unverdicted novelty 8.0

    For any CSP predicate R, unweighted CSP(R) instances admit sparsifiers of size at most their non-redundancy (up to polylog factors); weighted cases are pinned to chain length, via a VC-type theorem for set families us...

  2. Entropy methods in combinatorics

    math.CO 2026-07 accept novelty 2.0

    A selective survey of entropy methods in combinatorics, detailing randomized chain rules, Shearer's inequality, random homomorphisms, Pinsker-type arguments, the union-closed sets breakthrough, and entropy approaches ...