Some Properties of the $q$-Vietoris Number Sequence

Zehra Betül Gür; Serpil Halıcı

doi:10.53570/jnt.1778125

Some Properties of the $q$-Vietoris Number Sequence

Abstract

This study aims to present the $q$-Vietoris numbers, a generalization of the Vietoris numbers, by using quantum calculus ($q$-calculus) and to investigate some of their algebraic properties, such as recurrence relations, a representation with the $q$-Gamma function, and some essential identities. Furthermore, it derives some finite summation formulas involving the $q$-harmonic numbers and the $q$-Vietoris numbers. Finally, the study discusses the need for further research.

Keywords

Vietoris numbers, central binomial coefficients, $q$-identities, harmonic numbers

Supporting Institution

Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Thanks

The first author is supported by the 2211-A Domestic Doctoral Fellowship by the Scientific and Technological Research Council of Türkiye (TÜBİTAK), Grant number: 1649B032102384.

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Zehra Betül Gür ^*
0000-0002-3685-4222
Türkiye

Serpil Halıcı
0000-0002-8071-0437
Türkiye

Publication Date

December 31, 2025

Submission Date

September 5, 2025

Acceptance Date

November 17, 2025

Published in Issue

Year 2025 Number: 53

DOI

https://doi.org/10.53570/jnt.1778125

IZ

https://izlik.org/JA66XE57HF

APA

Gür, Z. B., & Halıcı, S. (2025). Some Properties of the $q$-Vietoris Number Sequence. Journal of New Theory, 53, 36-46. https://doi.org/10.53570/jnt.1778125

AMA

1.Gür ZB, Halıcı S. Some Properties of the $q$-Vietoris Number Sequence. JNT. 2025;(53):36-46. doi:10.53570/jnt.1778125

Chicago

Gür, Zehra Betül, and Serpil Halıcı. 2025. “Some Properties of the $q$-Vietoris Number Sequence”. Journal of New Theory, nos. 53: 36-46. https://doi.org/10.53570/jnt.1778125.

EndNote

Gür ZB, Halıcı S (December 1, 2025) Some Properties of the $q$-Vietoris Number Sequence. Journal of New Theory 53 36–46.

IEEE

[1]Z. B. Gür and S. Halıcı, “Some Properties of the $q$-Vietoris Number Sequence”, JNT, no. 53, pp. 36–46, Dec. 2025, doi: 10.53570/jnt.1778125.

ISNAD

Gür, Zehra Betül - Halıcı, Serpil. “Some Properties of the $q$-Vietoris Number Sequence”. Journal of New Theory. 53 (December 1, 2025): 36-46. https://doi.org/10.53570/jnt.1778125.

JAMA

1.Gür ZB, Halıcı S. Some Properties of the $q$-Vietoris Number Sequence. JNT. 2025;:36–46.

MLA

Gür, Zehra Betül, and Serpil Halıcı. “Some Properties of the $q$-Vietoris Number Sequence”. Journal of New Theory, no. 53, Dec. 2025, pp. 36-46, doi:10.53570/jnt.1778125.

Vancouver

1.Zehra Betül Gür, Serpil Halıcı. Some Properties of the $q$-Vietoris Number Sequence. JNT. 2025 Dec. 1;(53):36-4. doi:10.53570/jnt.1778125