Juanjo Ru'e

collaborators

3 papers

math.CO2026

Counting subsets of integers free of arithmetic configurations

Patrick Morris, Miquel Ortega, Juanjo RuÃ©

Cameron and ErdÅs asked if the number of sets free of arithmetic progressions of length $k$ is $2^{r_{k} (n) (1 + o (1))}$ , where $r_{k} (n)$ is the maximum cardinality of a $k$ -AP-free sub…

math.CO2024

On the chromatic number of powers of subdivisions of graphs

Michael Anastos, Simona Boyadzhiyska, Silas Rathke +1

For a given graph $G = (V, E)$ , we define its \emph{ $n$ th subdivision} as the graph obtained from $G$ by replacing every edge by a path of length $n$ . We also define the \emph{ $m$ th p…

math.CO2024

Product-free sets in the free group

We prove that product-free sets of the free group over a finite alphabet have maximum density $1/2$ with respect to the natural measure that assigns total weight one to each set of…