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Sam Mattheus

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Preprint Aug 2026

There are no sharply transitive subsets of $\mathrm{SL}(2,q)$ for $q\ge 13$

It was known at least to L.E. Dickson in 1901 that $\mathrm{SL}(2,q)$, in its natural action on $\mathbb{F}_q^2\setminus\{0\}$, has a sharply transitive subgroup only when $q\in\{2,3,5,7,11\}$. For $q$ prime, this result stems from Galois'letter to Chevalier in 1832. We extend this result to sharply transitive subsets...

J. Bamberg, Sam Mattheus · 0 citations
Preprint Aug 2026

An improved algebraic construction for Ramsey numbers

We provide an explicit algebraic construction showing that, uniformly for integers $3 \leq s \leq t$, as $t \to \infty$, \[ R( s,t ) \geq t^{(1-o(1)) \log s / \log(\log s + 1) }. \] For large fixed $s$, this improves the dependence on $s$ in the general off-diagonal construction of Alon and Pudl\'ak. In particular, $R(...

F. Ihringer, Sam Mattheus · 3 citations · ⚡1

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