Author

C. Schildkraut

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Preprint Aug 2026

Forcible groups and Frattini covers

We say that a finite group $G$ *forces* a finite group $H$ if every finite cover of $G$ contains a subgroup isomorphic to $H$, and we say $H$ is *forcible* if some finite group $G$ forces $H$. Complementing a classical result of Thompson--Mann, and answering a recent question of the third author, we show that a finite...

Sean Eberhard, R. Guralnick, C. Schildkraut et al. · 0 citations

Preprint Aug 2026

A new lower bound for two-color van der Waerden numbers

The van der Waerden number $w(k)$ is the smallest positive integer $N$ such that every two-coloring of $\{1,2,\ldots,N\}$ contains a monochromatic $k$-term arithmetic progression. We prove that $w(k) \geq (1-o(1))k2^{k-1}$ holds for all positive integers $k$. This verifies a conjecture of Erd\H{o}s. In 1968, Berlekamp...

Marcelo Campos, Jacob Fox, C. Schildkraut · 0 citations