József Balogh

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20232026

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math.CO2025

Maximal independent sets in the middle two layers of the Boolean lattice

József Balogh, Ce Chen, Ramon I. Garcia

Let $B (2 d - 1, d)$ be the subgraph of the hypercube $Q_{2 d - 1}$ induced by its two largest layers. Duffus, Frankl and Rödl proposed the problem of finding the asymptotics fo…

math.CO2025

Maximum number of points in general position in a random subset of finite $3$ -dimensional spaces

József Balogh, Haoran Luo

Let $α (F_{q}^{d}, p)$ be the maximum possible size of a point set in general position in the $p$ -random subset of $F_{q}^{d}$ . In this note, we determine the order of ma…

Maximal independent sets in the middle two layers of the Boolean lattice

Maximum number of points in general position in a random subset of finite 3-dimensional spaces

Maximum number of points in general position in a random subset of finite $3$ -dimensional spaces