The sandglass conjecture beyond cancellative pairs
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914014104125440 |
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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 |