Research Article

Groupoid and Semigroup Construction on Isosceles Triangular Numbers

Volume: 11 Number: 2 November 29, 2024
EN TR

Groupoid and Semigroup Construction on Isosceles Triangular Numbers

Abstract

Basic information about figurative numbers is provided. Then, information about isosceles triangular numbers, one of the two-dimensional figurative numbers, is given. It also includes information about algebraic structures and their definitions. Additionally, a binary operation that includes k -isosceles triangular numbers is presented, and the study investigates whether the algebraic structures defined with this operation form a groupoid or semigroup. Also, two examples are given that satisfy the results at the end of the paper.

Keywords

References

  1. Deza, E., & Deza, M. M., (2012). Figurate Numbers, World Scientific Publishing Co. Pte. Ltd., Singapore.
  2. Jitman, S., Awachai, K., & Tanla, P., (2017). Isosceles Triangular Numbers, Mathematical Journal-Math, 62(692), 39-49.
  3. Jitman, S. & Punpim, J., (2021). Characterizations And Identities For Isosceles Triangular Numbers, European Journal of Pure and Applied Mathematics, 14(2), 380-395.
  4. Sparavigna, A. C., (2019). Groupoids of OEIS A003154 Numbers (Star Numbers or Centered Dodecagonal Numbers), Zenodo.
  5. Sparavigna, A. C., (2019). Groupoids of OEIS A093112 and A093069 Numbers (oblong and odd square numbers), Zenodo.
  6. Emin, A., (2021). Semigroup Construction on Polygonal Numbers, Journal of Engineering Technology and Applied Sciences, 6(3), 143-153.
  7. Emin, A., (2022). Some Algebraic Structure on Figurate Numbers, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 11(2), 604-612.
  8. Rosenfeld, A., (1968). An Introduction to Algebraic Structures. New York: Holden-Day.

Details

Primary Language

English

Subjects

Group Theory and Generalisations

Journal Section

Research Article

Publication Date

November 29, 2024

Submission Date

June 12, 2023

Acceptance Date

October 26, 2023

Published in Issue

Year 2024 Volume: 11 Number: 2

APA
Emin, A., & Sarp, Ü. (2024). Groupoid and Semigroup Construction on Isosceles Triangular Numbers. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 11(2), 325-334. https://doi.org/10.35193/bseufbd.1313160
AMA
1.Emin A, Sarp Ü. Groupoid and Semigroup Construction on Isosceles Triangular Numbers. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2024;11(2):325-334. doi:10.35193/bseufbd.1313160
Chicago
Emin, Ahmet, and Ümit Sarp. 2024. “Groupoid and Semigroup Construction on Isosceles Triangular Numbers”. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 11 (2): 325-34. https://doi.org/10.35193/bseufbd.1313160.
EndNote
Emin A, Sarp Ü (November 1, 2024) Groupoid and Semigroup Construction on Isosceles Triangular Numbers. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 11 2 325–334.
IEEE
[1]A. Emin and Ü. Sarp, “Groupoid and Semigroup Construction on Isosceles Triangular Numbers”, Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, vol. 11, no. 2, pp. 325–334, Nov. 2024, doi: 10.35193/bseufbd.1313160.
ISNAD
Emin, Ahmet - Sarp, Ümit. “Groupoid and Semigroup Construction on Isosceles Triangular Numbers”. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 11/2 (November 1, 2024): 325-334. https://doi.org/10.35193/bseufbd.1313160.
JAMA
1.Emin A, Sarp Ü. Groupoid and Semigroup Construction on Isosceles Triangular Numbers. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2024;11:325–334.
MLA
Emin, Ahmet, and Ümit Sarp. “Groupoid and Semigroup Construction on Isosceles Triangular Numbers”. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, vol. 11, no. 2, Nov. 2024, pp. 325-34, doi:10.35193/bseufbd.1313160.
Vancouver
1.Ahmet Emin, Ümit Sarp. Groupoid and Semigroup Construction on Isosceles Triangular Numbers. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2024 Nov. 1;11(2):325-34. doi:10.35193/bseufbd.1313160