Miquel Ortega

collaborators

4 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.CO2026

A sparse canonical van der Waerden theorem

JosÃ© 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…

math.CO2026

Monochromatic products in random integer sets

Roger LidÃ³n, DarÃo MartÃnez, 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.CO2024

On the number of monochromatic solutions to multiplicative equations

Lucas AragÃ£o, Jonathan Chapman, Miquel Ortega +1

The following question was asked by Prendiville: given an $r$ -colouring of the interval ${2, \dots, N}$ , what is the minimum number of monochromatic solutions of the equation $x…