Author

Felix Christian Clemen

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Preprint Sep 2026

On the number of regular simplices in odd dimensions

Let $S^k_d(n)$ denote the maximum number of regular $(k-1)$-simplices spanned by $n$ points in $\mathbb{R}^d$. For all fixed $r\geq k\geq3$, the exact value of $S^k_{2r}(n)$ was recently determined by Dumitrescu and the authors for all sufficiently large $n$ when $k=3$, and conditionally on an optimization problem when...

Felix Christian Clemen, Dingyuan Liu · 0 citations

Preprint Aug 2026

Triangle-Saturated Graphs in the Semi-Random Graph Process

The semi-random graph process is an adaptive random graph process in which an online algorithm is initially given an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the algorithm independently and uniformly at random. The algorithm then adaptively selects a vertex $v$, and adds the edge $uv$ to...

Felix Christian Clemen, Paweł Prałat · 0 citations