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Fishburn Latent-Subset Conjecture

The Fishburn latent-subset conjecture states that every dual intersecting family F subset= 2^([n]) has some i in [n] satisfying the inequality below. Such a family obeys A intersection A^'!=emptyset and A union A^'!=[n] for all A,A^' in F. The family of lower latent subsets of F is

F^L={T subset= [n]:T not in F, T subset= A for some A in F}.

For i in [n], let F(i)={A in F:i in A} and F^L(i)={T in F^L:i in T}. The asserted inequality is

|F^L(i)|>=|F(i)|.

Dong and Mao (2026) proved the conjecture using the weighted star inequality of Chang, Liu, and Liu. Dong and Mao (2026) state that GPT-6 Astra found the proof following an approach suggested by the author. They also state that the author simplified and rewrote the proof and takes responsibility for the result.

See also

Power Set, Subset

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References

Dong, Y. and Mao, J. "Proof of Fishburn's Latent-Subset Conjecture." 28 Sep 2026. https://arxiv.org/abs/2609.35920.

Cite this as:

Weisstein, Eric W. "Fishburn Latent-Subset Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FishburnLatent-SubsetConjecture.html

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