Öz
In this study, some information about figurate numbers and centered polygonal numbers are given. Also, a general binary operator that includes all centered polygonal numbers is defined and it is investigated whether the algebraic structures defined with the general binary operator specify a groupoid and semigroup or not. And finally, some examples are given on the subject.
Anahtar Kelimeler
Figurate numbers Centered polygonal numbers Algebraic structure Binary operator.
Kaynakça
- Deza E., Deza M.M. 2012. Figurate Numbers. World Scientific Publishing, Singapore, 1-456.
- Sparavigna A. C. 2019. Groupoids of OEIS A003154 Numbers (star numbers or centered dodecagonal numbers). Zenodo, doi: 10.5281/zenodo.3387054.
- Sparavigna A. C. 2019. Groupoids of OEIS A093112 and A093069 Numbers (oblong and odd square numbers). Zenodo, doi: 10.5281/zenodo.3247003.
- Sparavigna A. C. 2018. On a generalized sum of the Mersenne Numbers. Zenodo, doi: 10.5281/zenodo.2634312.
- Emin A. 2021. Semigroup Construction on Polygonal Numbers. Journal of Engineering Technology and Applied Sciences, 6 (3): 143-153.
- Ateş F., Emin A. 2021. Some New Results on the Orthodox, Strongly π- Inverse and π- regularity of Some Monoids. Bulletin of The Society of Mathematicians Banja Luka, 11 (3): 463-472.
- Emin A., Ateş F., Ikikardes S., Cangul I.N. 2013. A new monoid constructions under crossed products. Journal of Inequalities and Applications, 244 (1): 1-6.
- Ateş F. 2009. Some new monoid and group constructions under semidirect products. Ars. Combinatoria, 91: 203-218.
- Howie J. M. 1995. Fundamentals of Semigroup Theory. Clarendon Press, Oxford, 1-351.
- Stover C., Weisstein E. W. Groupoid. http://mathworld.wolfram.com/Groupoid.html. (Date of access: 01.01.2022).
- The On-Line Encyclopedia of Integer Sequences, OEIS Foundation Inc. http://oeis.org. (Date of access: 15.01.2022).
Öz
Bu çalışmada figürsel sayılar ve merkezil çokgensel sayılar hakkında bilgilendirme yapılmıştır. Ayrıca tüm merkezil çokgensel sayıları içeren cebirsel yapı üzerinde genel bir ikili işlem tanımlanarak bu ikili işlemin tanımlanan cebirsel yapı üzerinde bir groupoid ve yarı grup belirtip belirtmediği araştırılmıştır. Son olarak bu konuya uygun ve destekleyici nitelikte örneklere yer verilmiştir.
Anahtar Kelimeler
Figürsel sayılar Merkezil çokgensel sayılar Cebirsel yapılar İkili işlem.
Kaynakça
- Deza E., Deza M.M. 2012. Figurate Numbers. World Scientific Publishing, Singapore, 1-456.
- Sparavigna A. C. 2019. Groupoids of OEIS A003154 Numbers (star numbers or centered dodecagonal numbers). Zenodo, doi: 10.5281/zenodo.3387054.
- Sparavigna A. C. 2019. Groupoids of OEIS A093112 and A093069 Numbers (oblong and odd square numbers). Zenodo, doi: 10.5281/zenodo.3247003.
- Sparavigna A. C. 2018. On a generalized sum of the Mersenne Numbers. Zenodo, doi: 10.5281/zenodo.2634312.
- Emin A. 2021. Semigroup Construction on Polygonal Numbers. Journal of Engineering Technology and Applied Sciences, 6 (3): 143-153.
- Ateş F., Emin A. 2021. Some New Results on the Orthodox, Strongly π- Inverse and π- regularity of Some Monoids. Bulletin of The Society of Mathematicians Banja Luka, 11 (3): 463-472.
- Emin A., Ateş F., Ikikardes S., Cangul I.N. 2013. A new monoid constructions under crossed products. Journal of Inequalities and Applications, 244 (1): 1-6.
- Ateş F. 2009. Some new monoid and group constructions under semidirect products. Ars. Combinatoria, 91: 203-218.
- Howie J. M. 1995. Fundamentals of Semigroup Theory. Clarendon Press, Oxford, 1-351.
- Stover C., Weisstein E. W. Groupoid. http://mathworld.wolfram.com/Groupoid.html. (Date of access: 01.01.2022).
- The On-Line Encyclopedia of Integer Sequences, OEIS Foundation Inc. http://oeis.org. (Date of access: 15.01.2022).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2022 |
| Gönderilme Tarihi | 3 Şubat 2022 |
| Kabul Tarihi | 8 Haziran 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 11 Sayı: 2 |
