Internal and external partial difference families and cyclotomy
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.
Citation
Huczynska , S & Johnson , L 2023 , ' Internal and external partial difference families and cyclotomy ' , Discrete Mathematics , vol. 346 , no. 3 , 113295 . https://doi.org/10.1016/j.disc.2022.113295
Publication
Discrete Mathematics
Status
Peer reviewed
ISSN
0012-365XType
Journal article
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Related items
Showing items related by title, author, creator and subject.
-
New constructions for disjoint partial difference families and external partial difference families
Huczynska, Sophie; Johnson, Laura (2024-04) - Journal articleRecently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously generalize partial difference sets, disjoint ... -
Statistical and agent-based modelling of the transmissibility of different SARS-CoV-2 variants in England and impact of different interventions
Panovska-Griffiths, J.; Swallow, B.; Hinch, R.; Cohen, J.; Rosenfeld, K.; Stuart, R. M.; Ferretti, L.; Di Lauro, F.; Wymant, C.; Izzo, A.; Waites, W.; Viner, R.; Bonell, C.; Fraser, C.; Klein, D.; Kerr, C. C.; The COVID-19 Genomics UK (COG-UK) Consortium (2022-10-03) - Journal articleThe English SARS-CoV-2 epidemic has been affected by the emergence of new viral variants such as B.1.177, Alpha and Delta, and changing restrictions. We used statistical models and the agent-based model Covasim, in June ... -
Different soluble aggregates of Aβ42 can give rise to cellular toxicity through different mechanisms
De, Suman; Wirthensohn, David C; Flagmeier, Patrick; Hughes, Craig; Aprile, Francesco A; Ruggeri, Francesco S; Whiten, Daniel R; Emin, Derya; Xia, Zengjie; Varela, Juan A; Sormanni, Pietro; Kundel, Franziska; Knowles, Tuomas P J; Dobson, Christopher M; Bryant, Clare; Vendruscolo, Michele; Klenerman, David (2019-04-04) - Journal articleProtein aggregation is a complex process resulting in the formation of heterogeneous mixtures of aggregate populations that are closely linked to neurodegenerative conditions, such as Alzheimer's disease. Here, we find ...