The existence problem of difference sets

Year 2022, , 917 - 922, 15.07.2022

Emek Demirci Akarsu , Safiye Öztürk

https://doi.org/10.17714/gumusfenbil.1105985

Abstract

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.

Keywords

Algorithm in MATLAB, Bruck Ryser Chowla theorem, Difference sets

Fark kümelerinin varlık problemi

Abstract

Fark kümelerinin gerçek hayat problemlerine uygulamaları arttıkça, bir grup üzerinde tanımlanan fark kümelerinin varlık problemi daha ilgi çekici hale gelmiştir. Fark kümelerinin birçok oluşturma metodu vardır: parametreler arası ilişkiler, fark kümelerinin var olmama teoremi (Bruck Ryser Chowla Teoremi), çarpanlar vb. Simetrik tasarım için benzer bir problem yine Bruck Ryser Chowla Teoremi'nin araştırılmasıyla yazarlar tarafından çalışılmıştır (Sakarya Üniversitesi Bilim Dergisi). Bu makalede fark kümelerinin varlık problemini; fark kümelerinin parametrelerini, BRC Teoremini ve MATLAB'da yazılmış bir algoritmayı kullanarak daha genel bir açıyla inceliyoruz.

Keywords

MATLAB algoritma, Bruck Ryser Chowla teoremi, Fark kümeleri

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