Internal and external partial difference families and cyclotomy |
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Institution: | School of Mathematics & Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland, UK |
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Abstract: | We introduce the concept of a disjoint partial difference family (DPDF) and an external partial difference family (EPDF), a natural generalization of the much-studied disjoint difference family (DDF), external difference family (EDF) and partial difference set (PDS). We establish properties and indicate connections to other recently-studied combinatorial structures. We show how DPDFs and EPDFs may be formed from PDSs, and present various cyclotomic constructions for DPDFs and EPDFs. As part of this, we develop a unified cyclotomic framework, which yields some known results on PDSs, DDFs and EDFs as special cases. |
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Keywords: | Disjoint partial difference family External partial difference family Disjoint difference family External difference family Partial difference set Cyclotomy |
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