Balancing Polynomials Under Permutations
| dc.contributor.author | Penner, Georgia | |
| dc.date.accessioned | 2024-03-16T17:52:21Z | |
| dc.date.available | 2024-03-16T17:52:21Z | |
| dc.date.issued | 2024 | |
| dc.description.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. | |
| dc.description.reviewstatus | Reviewed | |
| dc.description.scholarlevel | Undergraduate | |
| dc.description.sponsorship | Jamie Cassels Undergraduate Research Awards (JCURA) | |
| dc.identifier.uri | https://hdl.handle.net/1828/16166 | |
| dc.language.iso | en | |
| dc.publisher | University of Victoria | |
| dc.subject | Combinatorics | |
| dc.subject | Permutations | |
| dc.subject | Polynomials | |
| dc.subject | Symmetric functions | |
| dc.title | Balancing Polynomials Under Permutations | |
| dc.type | Poster |