PreprintCC BY 4.0arXiv
On cancellative pairs of families of subsets
Abstract
A pair (𝒜, ℬ) of families of subsets of [n] is cancellative if whenever A, A' ∈ 𝒜, B ∈ ℬ satisfy A ∪ B=A' ∪ B, then A=A', and whenever A ∈ 𝒜, B, B' ∈ ℬ satisfy A ∪ B=A ∪ B', then B=B'. We show that for every cancellative pair (𝒜, ℬ), the inequality |𝒜||ℬ| ≤ 2.25n holds, matching Tolhuizen's (2.25−o(1))n lower bound construction.
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BibTeX
@misc{fang2026cancellative,
title = {{On cancellative pairs of families of subsets}},
author = {Yijia Fang and Hao Huang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01483},
eprint = {2609.01483},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01483},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On cancellative pairs of families of subsets
AU - Yijia Fang
AU - Hao Huang
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.01483
UR - https://arxiv.org/abs/2609.01483
AB - A pair (𝒜, ℬ) of families of subsets of [n] is cancellative if whenever A, A' ∈ 𝒜, B ∈ ℬ satisfy A ∪ B=A' ∪ B, then A=A', and whenever A ∈ 𝒜, B, B' ∈ ℬ satisfy A ∪ B=A ∪ B', then B=B'. We show that for every cancellative pair (𝒜, ℬ), the inequality |𝒜||ℬ| ≤ 2.25^n holds, matching Tolhuizen's (2.25−o(1))^n lower bound construction.
ER -