论文标题
内部和外部差异家庭和环骨术
Internal and external partial difference families and cyclotomy
论文作者
论文摘要
我们介绍了不相交的部分差异家族（DPDF）和外部部分差异家族（EPDF）的概念，这是对遥不可及的差异差异家族（DDF），外部差异家族（EDF）和部分差异集和部分差异集（PDS）的自然概括。我们建立属性和构造，并指示与其他最近研究的组合结构的联系。我们展示了如何从PDS的集合中形成DPDF和EPDF，并呈现循环方法，产生DPDFS和EPDF的组件集不在一般的PDS中。作为其中的一部分，我们开发了一个统一的框架，其中包括各种已知的环流差异结构的构造，这也为DDF和EDF提供了新的结果。
We introduce the concept of a disjoint partial difference family (DPDF) and an external partial difference family (EPDF), a natural generalisation of the much-studied structures of disjoint difference family (DDF), external difference family (EDF) and partial difference set (PDS). We establish properties and constructions, and indicate connections to other recently-studied combinatorial structures. We show how DPDFs and EPDFs may be formed from collections of PDSs, and also present cyclotomic methods yielding DPDFs and EPDFs whose component sets are not in general PDSs. As part of this, we develop a unified framework encompassing various known constructions for cyclotomic difference structures, which also yields new results on DDFs and EDFs.
