PreprintCC0arXiv
Proof of Fishburn's latent-subset conjecture
Abstract
Fishburn's latent-subset conjecture, proposed in 1987 and revisited in 1988, asserts that for every dual intersecting family ℱ⊆ 2[n], there exists i∈[n] such that |ℱL(i)|≥|ℱ(i)|. Here ℱL is the family of the subsets of members of ℱ that do not belong to ℱ. In this paper, we prove the conjecture using the recent weighted star inequality of Chang, Liu, and Liu.
Related
BibTeX
@misc{dong2026proof,
title = {{Proof of Fishburn's latent-subset conjecture}},
author = {Yuxian Dong and Jianxi Mao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35920},
eprint = {2609.35920},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35920},
note = {CC0},
}
RIS
TY - UNPB
TI - Proof of Fishburn's latent-subset conjecture
AU - Yuxian Dong
AU - Jianxi Mao
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35920
UR - https://arxiv.org/abs/2609.35920
AB - Fishburn's latent-subset conjecture, proposed in 1987 and revisited in 1988, asserts that for every dual intersecting family ℱ⊆ 2^[n], there exists i∈[n] such that |ℱ^L(i)|≥|ℱ(i)|. Here ℱ^L is the family of the subsets of members of ℱ that do not belong to ℱ. In this paper, we prove the conjecture using the recent weighted star inequality of Chang, Liu, and Liu.
ER -