Semigroup Construction on Polygonal Numbers

Year 2021, Volume: 6 Issue: 3, 143 - 153, 31.12.2021

Ahmet Emin

https://doi.org/10.30931/jetas.1028567

Cited By: 1

Abstract

In this paper, some information about polygonal numbers are given. Also, a general binary operator that includes all polygonal numbers are given and it is investigated whether the algebraic structures defined with the general operator specify a semigroup or not.

Keywords

Polygonal numbers, binary operation, semigroup, monoid

References

• [1] Deza, E., Deza, M. M., “Figurate Numbers”, World Scientific Publishing, Singapore, (2012).
• [2] Sparavigna, A. C., “On a generalized sum of the Mersenne Numbers”, Zenodo. http://doi.org/10.5281/zenodo.1250048, (2018).
• [3] Sparavigna, A. C., “Groupoids of OEIS A093112 and A093069 Numbers (oblong and odd square numbers)”, Zenodo. http://doi.org/10.5281/zenodo.3247003, (2019).
• [4] Sparavigna, A. C., “Groupoids of OEIS A003154 Numbers (star numbers or centered dodecagonal numbers)”, Zenodo. http://doi.org/10.5281/zenodo.3387054, (2019).
• [5] Ateş, F., Emin, A., “Some New Results on the Orthodox, Strongly 𝜋𝜋- Inverse and 𝜋𝜋-Regularity of Some Monoids”, Bulletin of The Society of Mathematicians Banja Luka, 11(3) (2021) : 463-472.
• [6] Ateş, F., “Some new monoid and group constructions under semidirect products”, Ars. Combinatoria, 91 (2009) : 203-218.
• [7] Emin, A., Ateş, F., “A new monoid construction under crossed products”, Journal of Inequalities and Applications, 244(1) (2013).
• [8] Howie, J. M., “Fundamentals of Semigroup Theory”, No 12, Clarendon Press, Oxford, (1995).
• [9] Stover, C., Weisstein, E. W., “Groupoid” Retrieved in January, 30, 2021 from http://mathworld.wolfram.com/Groupoid.html, (2021).
• [10] The On-Line Encyclopedia of Integer Sequences, OEIS Foundation Inc., http://oeis.org, (2021).