Kreher, D.L. and Paterson, Maura B. and Stinson, D.R. (2025) Strong external difference families and classification of α-valuations. Journal of Combinatorial Designs , ISSN 1520-6610. (In Press)
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Abstract
One method of constructing (a2 + 1, 2, a, 1)-SEDFs (i.e., strong external difference families) in Za2+1 makes use of α-valuations of complete bipartite graphs Ka,a. We explore this approach and we provide a classification theorem which shows that all such α-valuations can be constructed recursively via a sequence of “blow-up” operations. We also enumerate all (a2 +1, 2, a, 1)-SEDFs in Za2+1 for a ≤ 14 and we show that all these SEDFs are equivalent to α-valuations via affine transformations. Whether this holds for all a > 14 as well is an interesting open problem. We also study SEDFs in dihedral groups, where we show that two known constructions are equivalent.
Metadata
| Item Type: | Article |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Maura Paterson |
| Date Deposited: | 23 Apr 2025 13:36 |
| Last Modified: | 29 Apr 2025 16:19 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/55413 |
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