D. Menezes

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math.CO2026

The Three-Dimensional Erdős Box Problem Has Exponent $11/4$

Dean Menezes

Let $z (n)$ be the maximum number of edges in a tripartite $3$ -uniform hypergraph with $n$ vertices in each part and no copy of $K_{2, 2, 2}^{(3)}$ (a ``box''). Erdős (1964) proved th…

math.CO2026

Sharp Bounds for Discrete Cube Skeleta

Dean Menezes

Fix integers $0 \leq k < n$ . Let $F_{n, k} (N)$ be the least size of a finite set $B \subset Z^{n}$ that contains a filled axis-parallel cube $k$ -skeleton centered at each point of some $N…

The Three-Dimensional Erdős Box Problem Has Exponent 11/4

Sharp Bounds for Discrete Cube Skeleta

The Three-Dimensional Erdős Box Problem Has Exponent $11/4$