Patrick Morris

activity

20232026

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3 papers · 1 filter

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

A note on multicolour Ramsey numbers and random sphere graphs

Yamaan Attwa, Albert López Vidal, Patrick Morris

The Ramsey number $r (t; ℓ)$ is the smallest $n$ such that every $ℓ$ -coloring of the edges of $K_{n}$ gives a monochromatic $K_{t}$ . In recent years, there have been several impr…

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…