Extremal Chowla sets and their linear analogues: A human-AI mathematical investigation using Co-Scientist

תקציר מקורי באנגליתarXiv:2607.24847v1 Announce Type: cross Abstract: We introduce an extremal invariant associated with Chowla-type order conditions in finite groups. A nonempty subset $S$ of a finite group $G$ is called a Chowla set if every element of $S$ has order greater than $|S|$, and we write $\Ccal(G)$ for the maximum cardinality of such a set. We first show that $\Ccal(G)$ is determined by the distribution of element orders in $G$. For cyclic groups, we derive an exact divisor formula and characterize the integers $n$ for which $\Ccal(\mathbb Z/n\mathbb Z)=\varphi(n)$. We prove that $\liminf_{n\to\infty}\Ccal(\mathbb Z/n\mathbb Z)/\varphi(n)=1$, whereas $\limsup_{n\to\infty}\Ccal(\mathbb Z/n\mathbb Z)/\varphi(n)=\infty$, and we determine the corresponding lower and upper limits under normalization b