Applications of Hypergroup Theory in Solving the Rubik's Cube

Yıl 2023, , 2068 - 2092, 01.09.2023

Burcu Nişancı Türkmen , Gamze Ela Kukuş

https://doi.org/10.21597/jist.1268544

Öz

The solution of the Rubik's cube was designed with an algebraic structure different from the group algebraic structure existing in the literature with the help of hypergroups. The generalized permutation hypergroup concept has been adopted as the method by which the strategy of the Rubik's cube solution will develop; carried out with the development of methods applied in group theory. Although there are inadequacies in the application of abstract algebra studies all over the world, with this study, the basis of the analysis of the Rubik's cube with the help of hypergroups was obtained; Thus, it has been contributed to national and international academic research to be the application of the studies carried out in the field of abstract algebra in our country. Therefore, with the help of the Rubik's cube, it has been proven that the algebra studies in the literature can be translated into practice.

Anahtar Kelimeler

Group Theory, Rubik’s Cube, Hypergroup Theory

Destekleyen Kurum

TUBİTAK 2209-A

Proje Numarası

1919B012105753

Rubik Küpün Çözümlenmesinde Hiper Grup Teori Uygulamaları

Öz

Rubik küpünün çözümünün hiper gruplar yardımıyla literatürde var olan grup cebirsel yapısından farklı bir cebirsel yapıyla tasarımı sağlanmıştır. Rubik küp çözümünün stratejisinin gelişim kaydedeceği yöntem olarak genelleştirilmiş permütasyon hiper grup kavramı benimsenmiş olup; grup teoride uygulanan yöntemlerin geliştirilmesi ile gerçekleştirilmiştir. Soyut cebir çalışmalarının uygulama bulması konusunda tüm dünyada yetersizlikler mevcut olmasına rağmen bu çalışma ile Rubik küpün hiper gruplar yardımıyla çözümleme esası elde edilmiş; böylece ulusal ve uluslararası akademik araştırmalara, ülkemizdeki soyut cebir alanında yürütülen çalışmaların uygulaması olması hususunda katkı sunulmuştur. Dolayısıyla Rubik küp yardımıyla literatürde var olan cebir çalışmalarının uygulamaya dönüştürülebilir olduğu kanıtlanmıştır.

Anahtar Kelimeler

Hiper Grup Teorisi, Rubik Küp, Grup Teorisi

Proje Numarası

1919B012105753

Kaynakça

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