The sandglass conjecture beyond cancellative pairs

Fuente: arXiv
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Main Authors: Mond, Adva, Souza, Victor, Versteegen, Leo
Format: Preprint
Published: 2025
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author Mond, Adva
Souza, Victor
Versteegen, Leo
author_facet Mond, Adva
Souza, Victor
Versteegen, Leo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_21819
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The sandglass conjecture beyond cancellative pairs
Mond, Adva
Souza, Victor
Versteegen, Leo
Combinatorics
05D05
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.
title The sandglass conjecture beyond cancellative pairs
topic Combinatorics
05D05
url https://arxiv.org/abs/2508.21819