A Noncommutative Chromatic Symmetric Function
| dc.creator | Gebhard, David D. | |
| dc.creator | Sagan, Bruce E. | |
| dc.date | 1999-07-12 | |
| dc.date.accessioned | 2026-07-07T05:29:52Z | |
| dc.date.available | 2026-07-07T05:29:52Z | |
| dc.description | Stanley associated with a graph G a symmetric function X_G which reduces to G's chromatic polynomial under a certain specialization of variables. He then proved various theorems generalizing results about the chromatic polynomial, as well as new ones that cannot be interpreted at that level. Unfortunately, X_G does not satisfy a Deletion-Contraction Law which makes it difficult to apply induction. We introduce a symmetric function in noncommuting variables which does have such a law and specializes to X_G when the variables are allowed to commute. This permits us to further generalize some of Stanley's theorems and prove them in a uniform and straightforward manner. Furthermore, we make some progress on the (3+1)-free Conjecture of Stanley and Stembridge. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/9907076 | |
| dc.identifier | http://arxiv.org/abs/math/9907076 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78811 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C15 | |
| dc.title | A Noncommutative Chromatic Symmetric Function | |
| dc.type | text |