Miquel Ortega

collaborators

3 papers

math.CO2026

Counting subsets of integers free of arithmetic configurations

Patrick Morris, Miquel Ortega, Juanjo Rué

Cameron and Erdős 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 subs…

math.CO2026

Monochromatic products in random integer sets

Roger Lidón, Darío Martínez, Patrick Morris +1

A well-known consequence of Schur's theorem is that for $r \in N$ , if $n$ is sufficiently large, then any $r$ -colouring of $[n]$ results in monochromatic $a, b, c \in [n]$ suc…

math.CO2025

A sparse canonical van der Waerden theorem

José D. Alvarado, Yoshiharu Kohayakawa, Patrick Morris +2

The canonical van der Waerden theorem asserts that, for sufficiently large $n$ , every colouring of $[n]$ contains either a monochromatic or a rainbow arithmetic progression of leng…