Gerardo L. Maldonado

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20212026

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math.CO2026

Disconnected graphs and extremal bounds for realizable distance orders

Gerardo L. Maldonado, Leonardo Martínez-Sandoval, Miguel Raggi +1

Let $G$ be a graph together with a total order $≺$ on its edges. We say that $≺$ is realizable in $R^{d}$ if there is a placement of the vertices of $G$ in $\mathbb{…

math.CO2024

On the orthogonal Grünbaum partition problem in dimension three

Gerardo L. Maldonado, Edgardo Roldán-Pensado

Grünbaum's equipartition problem asked if for any measure $μ$ on $R^{d}$ there are always $d$ hyperplanes which divide $R^{d}$ into $2^{d}$ $μ$ -equal parts. This proble…

math.CO2023

Total orders realizable as the distances between two sets of points

Gerardo L. Maldonado, Miguel Raggi Pérez, Edgardo Roldán-Pensado

In this note we give a negative answer to a question proposed by Almendra-Hernández and Martínez-Sandoval. Let $n \leq m$ be positive integers and let $X$ and $Y$ be sets of sizes $n…