Author

Haoran Luo

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Preprint Aug 2026

The number of sum-free subsets of lattice cubes

A subset of the $d$-dimensional lattice cube $[n]^d$ is sum-free if it contains no solution to the equation $x+y=z$. We study the total number of such subsets. For $d=1$, Cameron and Erd\H{o}s conjectured that the number of sum-free subsets of $[n]$ is $O(2^{n/2})$, and this was proved independently by Green and Sapozh...

Haoran Luo · 0 citations

Preprint Jul 2026

On the minimum size of maximal $k$-wise intersecting families

A family $\mathcal{F}$ of subsets of $[n] := \{1,2,\ldots, n\}$ is called maximal $k$-wise intersecting if every collection of at most $k$ members of $\mathcal{F}$ has a non-empty intersection, and adding any other set to $\mathcal{F}$ breaks this property. An old question by Erd\H{o}s and Kleitman from 1974 asks for t...

Haoran Luo · 0 citations