José Madrid

activity

20242026

collaborators

6 papers

math.DS2026

Translational tilings by axis-parallel polygonal sets

Jaume de Dios Pont, Jan Grebík, Rachel Greenfeld +1

The periodic tiling conjecture asserts that if a bounded set $Ω \subset R^{d}$ of finite measure tiles $R^{d}$ by translations, then it admits at least one fully periodi…

math.CA2026

On the frequency function of Hardy-Littlewood maximal functions

Carlos Garzón, José Madrid

We study the frequency function (introduced by Temur) in both the discrete and continuous settings. More precisely, we extend the definition of the frequency function to the higher…

math.CA2025

Optimal Young's convolutions inequality and its reverse form on the hypercube

David Beltran, Paata Ivanisvili, José Madrid +1

We establish sharp forms of Young's convolution inequality and its reverse on the discrete hypercube ${0, 1}^{d}$ in the diagonal case $p = q$ . As applications, we derive bounds for a…

math.CA2024

Sharp Poincare-Wirtinger inequalities on complete graphs

Cristian González-Riquelme, José Madrid

Let $K_{n} = (V, E)$ be the complete graph with $n \geq 3$ vertices (here $V$ and $E$ denote the set of vertices and edges of $K_{n}$ respectively). We find the optimal value ${\bf{C}}_{n,…

math.CO2024

Periodicity and decidability of translational tilings by rational polygonal sets

Jaume de Dios Pont, Jan Grebík, Rachel Greenfeld +1

The periodic tiling conjecture asserts that if a region $Σ \subset R^{d}$ tiles $R^{d}$ by translations then it admits at least one fully periodic tiling. This conjectur…

math.CO2024

Discrete Brunn-Minkowski Inequality for subsets of the cube

Lars Becker, Paata Ivanisvili, Dmitry Krachun +1

We show that for all $A, B \subseteq {0, 1, 2}^{d}$ we have $∣ A + B ∣ \geq (∣ A ∣∣ B ∣)^{l o g (5) / (2 l o g (3))} .$ We also show that for all finite $A, B \subset Z^{d}$ , and any $V…