English

The sandglass conjecture beyond cancellative pairs

Combinatorics 2025-09-01 v1

Abstract

The sandglass conjecture, posed by Simonyi, states that if a pair (A,B)(A, B) of families of subsets of [n][n] is recovering then AB2n|A| |B| \leq 2^n. We improve the best known upper bound to AB2.2543n|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.

Keywords

Cite

@article{arxiv.2508.21819,
  title  = {The sandglass conjecture beyond cancellative pairs},
  author = {Adva Mond and Victor Souza and Leo Versteegen},
  journal= {arXiv preprint arXiv:2508.21819},
  year   = {2025}
}

Comments

12 pages

R2 v1 2026-07-01T05:12:36.036Z