论文标题
团戒指和性格总和：交易技巧
Group rings and character sums: tricks of the trade
论文作者
论文摘要
组环设置与性格理论方法的组合可以通过其性格总和对各种组合结构进行优雅而强大的分析。这些组合结构包括差异集，相对差异集，局部差异集，弯曲功能，超平面，差距和LP包装。但是，有关这些技术的文献通常依赖于特殊的惯例和隐性理解，这些惯例并不总是很容易获得该主题的人。尽管有许多出色的高级资源来描述这些技术，但我们并不知道在入门级别上的说明性论文表达了常用的``贸易技巧''。我们试图通过说明性的例子，明确讨论惯例以及基本结果的有益的证据来纠正这种情况。
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets, relative difference sets, partial difference sets, bent functions, hyperplanes, spreads, and LP-packings. However, the literature on these techniques often relies on peculiar conventions and implicit understandings that are not always readily accessible to those new to the subject. While there are many excellent advanced sources describing these techniques, we are not aware of an expository paper at the introductory level that articulates the commonly used ``tricks of the trade''. We attempt to remedy this situation by means of illustrative examples, explicit discussion of conventions, and instructive proofs of fundamental results.
