Internal and external partial difference families and cyclotomy

Sophie Huczynska, Laura Johnson*

*Corresponding author for this work

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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.

Original languageEnglish
Article number113295
Number of pages24
JournalDiscrete Mathematics
Issue number3
Early online date28 Dec 2022
Publication statusPublished - 1 Mar 2023


  • Disjoint partial difference family
  • External partial difference familiy
  • Disjoint different family
  • External difference family
  • Partial difference set
  • Cyclotomy


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