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

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

Cite

RIS / Bibtex

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