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The existence problem of difference sets

Cilt: 12 Sayı: 3 15 Temmuz 2022
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The existence problem of difference sets

Öz

The existence problem of difference sets in a group becomes more interesting since the applications of difference sets on real life problems become more common. There are several construction methods for difference sets: the relation among parameters, nonexistence of difference sets (Bruck Ryser Chowla Theorem), multipliers etc. A similar problem for symmetric designs along with an investigation of Bruck Ryser Chowla theorem has been discussed by the writers (Sakarya University Journal of Science). In this paper, we study the existence problem of difference sets in a more general concept by using difference sets parameters, BRC Theorem, and an algorithm written in MATLAB.

Anahtar Kelimeler

Algorithm in MATLAB, Bruck Ryser Chowla theorem, Difference sets

Kaynakça

  1. Baumert, L. D. (1971). Cyclic difference sets. (Vol. 182). California Institute of Technology Pasadena CA/USA. ISBN: 978-3540053682.
  2. Bruck, R. H., & Ryser, H. J. (1949). The nonexistence of certain finite projective planes. Canadian Journal of Mathematics, 1(1), 88-93. https://doi.org/10.4153/CJM-1949-009-2
  3. Bruck, R. H. (1955). Difference sets in a finite group, Transactions of the American Mathematical Society, 78(2), 464-481. https://doi.org/10.2307/1993074
  4. Chowla, S., & Ryser, H. J. (1950). Combinatorial problems. Canadian Journal of Mathematics, 2, 93-99. https://doi.org/10.4153/CJM-1950-009-8
  5. Demirci Akarsu E., & Öztürk, S. (2022). An existence problem for symmetric design: Bruck Ryser Chowla theorem. Sakarya University Journal of Science, 26(2), 241-248, https://doi.org/10.16984/saufenbilder.962817
  6. Golomb, S. W. (1999). Construction of signals with favorable correlation properties, in difference sets , sequences and their correlation roperties. Kluwer Academic Publishers, 542(448), 159-194. https://doi.org/10.1007/978-94-011-4459-9_7
  7. Hall Jr, M. (1947). Cyclic projective planes. Duke Mathematical Journal, 14(4), https://doi.org/1079-1090. 10.1215/S0012-7094-47-01482-8
  8. Lander, E. S. (1983). Symmetric designs: An algebraic approach. (Vol.74). London Mathematical Society, Lecture Note Series. Cambridge University. ISBN: 978-0-52128693-0
  9. Lehmer, E. (1953). On residue difference sets. Canadian Journal of Mathematics, 5, 425-432. https://doi.org/10.4153/CJM-1953-047-3
  10. Morrice, R. T. (2015). Difference sets: An investigation into the properties and criteria for existence [Master thesis, Carleton University].

Kaynak Göster

APA
Demirci Akarsu, E., & Öztürk, S. (2022). The existence problem of difference sets. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 12(3), 917-922. https://doi.org/10.17714/gumusfenbil.1105985
AMA
1.Demirci Akarsu E, Öztürk S. The existence problem of difference sets. Gümüşhane Üniversitesi Fen Bilimleri Dergisi. 2022;12(3):917-922. doi:10.17714/gumusfenbil.1105985
Chicago
Demirci Akarsu, Emek, ve Safiye Öztürk. 2022. “The existence problem of difference sets”. Gümüşhane Üniversitesi Fen Bilimleri Dergisi 12 (3): 917-22. https://doi.org/10.17714/gumusfenbil.1105985.
EndNote
Demirci Akarsu E, Öztürk S (01 Temmuz 2022) The existence problem of difference sets. Gümüşhane Üniversitesi Fen Bilimleri Dergisi 12 3 917–922.
IEEE
[1]E. Demirci Akarsu ve S. Öztürk, “The existence problem of difference sets”, Gümüşhane Üniversitesi Fen Bilimleri Dergisi, c. 12, sy 3, ss. 917–922, Tem. 2022, doi: 10.17714/gumusfenbil.1105985.
ISNAD
Demirci Akarsu, Emek - Öztürk, Safiye. “The existence problem of difference sets”. Gümüşhane Üniversitesi Fen Bilimleri Dergisi 12/3 (01 Temmuz 2022): 917-922. https://doi.org/10.17714/gumusfenbil.1105985.
JAMA
1.Demirci Akarsu E, Öztürk S. The existence problem of difference sets. Gümüşhane Üniversitesi Fen Bilimleri Dergisi. 2022;12:917–922.
MLA
Demirci Akarsu, Emek, ve Safiye Öztürk. “The existence problem of difference sets”. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, c. 12, sy 3, Temmuz 2022, ss. 917-22, doi:10.17714/gumusfenbil.1105985.
Vancouver
1.Emek Demirci Akarsu, Safiye Öztürk. The existence problem of difference sets. Gümüşhane Üniversitesi Fen Bilimleri Dergisi. 01 Temmuz 2022;12(3):917-22. doi:10.17714/gumusfenbil.1105985