Toward the Determination of Vietoris-like Polynomials

Nurten Gürses; Duygu Çağlar Çay

doi:10.53570/jnt.1651994

EN

Toward the Determination of Vietoris-like Polynomials

Abstract

This paper studies the relationship between polynomials and classical number sequences, focusing on their structural properties and mathematical significance. It explores a specific class of polynomials inspired by Vietoris' number sequences, referred to as Vietoris-like polynomials. The primary objective is to analyze their fundamental algebraic properties, recurrence relations, and special identities. The study employs algebraic methods to derive the recurrence relations and explicit formulas for these polynomials. Moreover, it establishes Catalan-like, Cassini-like, and d'Ocagne-like identities.

Keywords

Polynomials, Vietoris, Vietoris-like polynomials

Supporting Institution

Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Thanks

The second author is supported by the 2211-A Domestic Doctoral Fellowship by the Scientific and Technological Research Council of Türkiye (TÜBİTAK), Grant number: 1649B032103711.

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Nurten Gürses ^*
0000-0001-8407-854X
Türkiye

Duygu Çağlar Çay
0000-0003-2036-9684
Türkiye

Early Pub Date

June 30, 2025

Publication Date

June 30, 2025

Submission Date

March 5, 2025

Acceptance Date

May 12, 2025

Published in Issue

Year 2025 Number: 51

DOI

https://doi.org/10.53570/jnt.1651994

IZ

https://izlik.org/JA95LB22GC

APA

Gürses, N., & Çağlar Çay, D. (2025). Toward the Determination of Vietoris-like Polynomials. Journal of New Theory, 51, 10-25. https://doi.org/10.53570/jnt.1651994

AMA

1.Gürses N, Çağlar Çay D. Toward the Determination of Vietoris-like Polynomials. JNT. 2025;(51):10-25. doi:10.53570/jnt.1651994

Chicago

Gürses, Nurten, and Duygu Çağlar Çay. 2025. “Toward the Determination of Vietoris-Like Polynomials”. Journal of New Theory, nos. 51: 10-25. https://doi.org/10.53570/jnt.1651994.

EndNote

Gürses N, Çağlar Çay D (June 1, 2025) Toward the Determination of Vietoris-like Polynomials. Journal of New Theory 51 10–25.

IEEE

[1]N. Gürses and D. Çağlar Çay, “Toward the Determination of Vietoris-like Polynomials”, JNT, no. 51, pp. 10–25, June 2025, doi: 10.53570/jnt.1651994.

ISNAD

Gürses, Nurten - Çağlar Çay, Duygu. “Toward the Determination of Vietoris-Like Polynomials”. Journal of New Theory. 51 (June 1, 2025): 10-25. https://doi.org/10.53570/jnt.1651994.

JAMA

1.Gürses N, Çağlar Çay D. Toward the Determination of Vietoris-like Polynomials. JNT. 2025;:10–25.

MLA

Gürses, Nurten, and Duygu Çağlar Çay. “Toward the Determination of Vietoris-Like Polynomials”. Journal of New Theory, no. 51, June 2025, pp. 10-25, doi:10.53570/jnt.1651994.

Vancouver

1.Nurten Gürses, Duygu Çağlar Çay. Toward the Determination of Vietoris-like Polynomials. JNT. 2025 Jun. 1;(51):10-25. doi:10.53570/jnt.1651994

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Some Properties of the $q$-Vietoris Number Sequence

Journal of New Theory

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