On the nonexistence of semi-regular relative difference sets
In this paper, we study semi-regular relative difference sets. We give some nonexistence results on abelian (mn,n,mn,m) relative difference sets. In particular, we focus on the case when m is prime and show that, for any fixed integer n≥2, there are at most finitely many primes p for which an abelia...
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sg-ntu-dr.10356-1703412023-09-08T02:12:55Z On the nonexistence of semi-regular relative difference sets Leung, Ka Hin Schmidt, Bernhard Zhang, Tao School of Physical and Mathematical Sciences Science::Mathematics Group Ring Weil Number In this paper, we study semi-regular relative difference sets. We give some nonexistence results on abelian (mn,n,mn,m) relative difference sets. In particular, we focus on the case when m is prime and show that, for any fixed integer n≥2, there are at most finitely many primes p for which an abelian (pn,n,pn,p) relative difference set may exist. We illustrate our results by investigating the existence of (mn,n,mn,m) relative difference sets with m∈{2,3,4} in detail. Ministry of Education (MOE) Research is supported by Ministry of Education grant R-146-000-158-112, MOE Academic Research Fund Tier 1 (RG27/18) and by the National Natural Science Foundation of China under Grant No. 11801109. 2023-09-08T02:12:55Z 2023-09-08T02:12:55Z 2023 Journal Article Leung, K. H., Schmidt, B. & Zhang, T. (2023). On the nonexistence of semi-regular relative difference sets. Journal of Combinatorial Theory, Series A, 193, 105674-. https://dx.doi.org/10.1016/j.jcta.2022.105674 0097-3165 https://hdl.handle.net/10356/170341 10.1016/j.jcta.2022.105674 2-s2.0-85144064760 193 105674 en RG27/18 R-146-000-158-112 Journal of Combinatorial Theory, Series A © 2022 Elsevier Inc. All rights reserved. |
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Science::Mathematics Group Ring Weil Number Leung, Ka Hin Schmidt, Bernhard Zhang, Tao On the nonexistence of semi-regular relative difference sets |
| description |
In this paper, we study semi-regular relative difference sets. We give some nonexistence results on abelian (mn,n,mn,m) relative difference sets. In particular, we focus on the case when m is prime and show that, for any fixed integer n≥2, there are at most finitely many primes p for which an abelian (pn,n,pn,p) relative difference set may exist. We illustrate our results by investigating the existence of (mn,n,mn,m) relative difference sets with m∈{2,3,4} in detail. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Leung, Ka Hin Schmidt, Bernhard Zhang, Tao |
| format |
Article |
| author |
Leung, Ka Hin Schmidt, Bernhard Zhang, Tao |
| author_sort |
Leung, Ka Hin |
| title |
On the nonexistence of semi-regular relative difference sets |
| title_short |
On the nonexistence of semi-regular relative difference sets |
| title_full |
On the nonexistence of semi-regular relative difference sets |
| title_fullStr |
On the nonexistence of semi-regular relative difference sets |
| title_full_unstemmed |
On the nonexistence of semi-regular relative difference sets |
| title_sort |
on the nonexistence of semi-regular relative difference sets |
| publishDate |
2023 |
| url |
https://hdl.handle.net/10356/170341 |
| _version_ |
1779156331510366208 |