Work

Symmetric Functions and Rings of Multinumbers Associated with Finite Groups

Year: 2024

Type: article

Abstract: In this paper, we introduce ωn-symmetric polynomials associated with the finite group ωn, which consists of roots of unity, and groups of permutations acting on the Cartesian product of Banach spaces ℓ1. These polynomials extend the classical notions of symmetric and supersymmetric polynomials on ℓ1. We explore algebraic bases in the algebra of ωn-symmetric polynomials and derive corresponding generating functions. Building on this foundation, we construct rings of multisets (multinumbers), defined as equivalence classes on the underlying space under the action of ωn-symmetric polynomials, and investigate their fundamental properties. Furthermore, we examine the ring of integer multinumbers associated with the group ωn, proving that it forms an integral domain when n is prime or n=4.

Source: Symmetry

DOI: 10.3390/sym17010033

Authors: Yurii Chopiuk, Andriy Zagorodnyuk

Institutions: Kyiv School of Economics, Vasyl Stefanyk Carpathian National University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: National Research Foundation of Ukraine