arXiv · 2609.01483
On cancellative pairs of families of subsets
Abstract
A pair $(\mathcal{A}, \mathcal{B})$ of families of subsets of $[n]$ is cancellative if whenever $A, A' \in \mathcal{A}, B \in \mathcal{B}$ satisfy $A \cup B=A' \cup B$, then $A=A'$, and whenever $A \in \mathcal{A}, B, B' \in \mathcal{B}$ satisfy $A \cup B=A \cup B'$, then $B=B'$. We show that for every cancellative pair $(\mathcal{A}, \mathcal{B})$, the inequality $|\mathcal{A}||\mathcal{B}| \le 2.25^n$ holds, matching Tolhuizen's $(2.25-o(1))^n$ lower bound construction.
Explore related subjects
Keep this discovery
Yijia Fang, Hao Huang. 2026-09-02. On cancellative pairs of families of subsets. https://arxiv.org/abs/2609.01483
Cite the original work for its findings. Save a collection to share your selection of sources.
Discover connections
Connections use source metadata and explicit phrase matches, not verified experimental comparisons.