Balancing Polynomials Under Permutations
Date
2024
Authors
Penner, Georgia
Journal Title
Journal ISSN
Volume Title
Publisher
University of Victoria
Abstract
Motivated by previous work by del Valle and Dukes on balancing matrices and multigraphs, we explore the equivalent problem on multivariate polynomials. The balancing number of a polynomial is loosely understood as the smallest number of permuted copies of a polynomial one needs to add together to obtain a symmetric polynomial. We are particularly interested in polynomials which have a balancing number of 1 but which aren’t already symmetric. In our work, we attempt to extend the results on matrices to the case of polynomials and we obtain a complete, simple characterization of the balancing numbers of polynomials in three variables.
Description
Keywords
Combinatorics, Permutations, Polynomials, Symmetric functions