Proof of Fishburn's latent-subset conjecture

Yuxian Dong; Jianxi Mao

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arXiv · 2609.35920

Proof of Fishburn's latent-subset conjecture

Yuxian Dong·Jianxi Mao

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Abstract

Fishburn's latent-subset conjecture, proposed in 1987 and revisited in 1988, asserts that for every dual intersecting family $\mathcal F\subseteq 2^{[n]}$, there exists $i\in[n]$ such that $|\mathcal F^L(i)|\geq|\mathcal F(i)|$. Here $\mathcal F^L$ is the family of the subsets of members of $\mathcal F$ that do not belong to $\mathcal F$. In this paper, we prove the conjecture using the recent weighted star inequality of Chang, Liu, and Liu.

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Yuxian Dong, Jianxi Mao. 2026-09-28. Proof of Fishburn's latent-subset conjecture. https://arxiv.org/abs/2609.35920

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