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The sandglass conjecture beyond cancellative pairs

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arxiv 2508.21819 v1 pith:VAICBANI submitted 2025-08-29 math.CO

The sandglass conjecture beyond cancellative pairs

classification math.CO
keywords pairscancellativeconjecturerecoveringsandglassupperbarrierbest
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The sandglass conjecture, posed by Simonyi, states that if a pair $(A, B)$ of families of subsets of $[n]$ is recovering then $|A| |B| \leq 2^n$. We improve the best known upper bound to $|A| |B| \leq 2.2543^n$. To do this we overcome a significant barrier by exponentially separating the upper bounds on recovering pairs from cancellative pairs, a related notion.

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