Toward the Determination of Vietoris-like Polynomials

Year 2025, Issue: 51, 10 - 25, 30.06.2025

Nurten Gürses , Duygu Çağlar Çay

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

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.

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