The $r$-Stirling Genocchi Numbers

Authors

  • Vernard Dechosa Mathematics Department, Cebu Normal University Cebu City, Philippines
  • Roberto Bagsarsa Corcino Research Institute for Computational Mathematics and Physics Cebu Normal University Cebu City, Philippines https://orcid.org/0000-0003-1681-1804

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.6202

Keywords:

Genocchi numbers, r-Stirling numbers, recurrence relations, generating function, Bernoulli numbers

Abstract

This paper introduces the \( r \)-Stirling Genocchi numbers, a new sequence derived by combining Broder's \( r \)-Stirling numbers with the classical Genocchi numbers, which are closely related to Bernoulli numbers and have notable applications in algebraic combinatorics. While the original \( r \)-Stirling numbers were developed using combinatorial methods to count set partitions, this study adopts an algebraic approach to explore the properties of the new sequence. Through tools like generating functions, recurrence relations, and algebraic transformations, the paper uncovers deeper structural insights and highlights the broader mathematical connections between partition theory, number theory, and combinatorial analysis.

Author Biography

  • Roberto Bagsarsa Corcino, Research Institute for Computational Mathematics and Physics Cebu Normal University Cebu City, Philippines

    Mathematics Department, Mathematics and Physics, Cebu Normal University, Cebu City, Philippines

Downloads

Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Number Theory

License

Copyright (c) 2025 Vernard Dechosa, Roberto Bagsarsa Corcino

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

The $r$-Stirling Genocchi Numbers. (2025). European Journal of Pure and Applied Mathematics, 18(2), 6202. https://doi.org/10.29020/nybg.ejpam.v18i2.6202