论文标题
Herzog-Schonheim猜想，统一和凸多边形的根源消失
Herzog-Schonheim conjecture, vanishing sums of roots of unity and convex polygons
论文作者
论文摘要
令$ g $为一个组，$ h_1 $，\ ldots，$ h_s $是$ g $ in Indices $ d_1，\ ldots，d_s $的子组。 1974年，M。Herzog和J.Schönheim认为，如果$ \ {h_iα_i\} _ {i = 1}^{i = s} $，$α_i\ in G $，是$ g $的coset分区，那么$ g $，那么$ d_1，\ d_1，\ ldots，\ ldots，d_s $是不同的。在本文中，我们将猜想作为消失的统一根和凸多边形总和的问题，并使用这种方法证明了一些结果。
Let $G$ be a group and $H_1$,\ldots,$H_s$ be subgroups of $G$ of indices $d_1,\ldots,d_s$ respectively. In 1974, M. Herzog and J. Schönheim conjectured that if $\{H_iα_i\}_{i=1}^{i=s}$, $α_i\in G$, is a coset partition of $G$, then $d_1,\ldots,d_s$ cannot be distinct. In this paper, we present the conjecture as a problem on vanishing sum of roots of unity and convex polygons and prove some results using this approach.
