Penner, Georgia2024-03-162024-03-162024https://hdl.handle.net/1828/16166Motivated 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.enCombinatoricsPermutationsPolynomialsSymmetric functionsPoster