Work

Complete Homogeneous Symmetric Polynomials and Generalized Vieta’s Formulas

Year: 2026

Type: article

Abstract: We generalize the classical Vieta formulas that express the coefficients of a polynomial in terms of all the roots. In particular, we focus on the case when just some of the roots are known. Our formulas are established by exploiting some properties of the complete homogeneous symmetric polynomials. Further, we provide new identities for these polynomials when the variables are in a geometric progression and new identities involving the roots of unity.

Source: Results in Mathematics

DOI: 10.1007/s00025-026-02632-5

Authors: Laura De Carli, Andrew Echezabal, Maurizio Laporta

Institutions: Florida International University, University of Naples Federico II

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Università degli Studi di Napoli Federico II