dc.contributor.author | Crew, Logan | |
dc.contributor.author | Haithcock, Evan | |
dc.contributor.author | Reynes, Josephine | |
dc.contributor.author | Spirkl, Sophie | |
dc.date.accessioned | 2024-05-24 14:59:32 (GMT) | |
dc.date.available | 2024-05-24 14:59:32 (GMT) | |
dc.date.issued | 2024-07 | |
dc.identifier.uri | https://doi.org/10.1016/j.aam.2024.102718 | |
dc.identifier.uri | http://hdl.handle.net/10012/20593 | |
dc.description | This is an open access article under the CC BY license (http://creativecommons.org /licenses/by /4.0/). | en |
dc.description.abstract | In this paper, we extend the chromatic symmetric function X to a chromatic k-multisymmetric function Xk, defined for graphs equipped with a partition of their vertex set into k parts. We demonstrate that this new function retains the basic properties and basis expansions of X, and we give a method for systematically deriving new linear relationships for X from previous ones by passing them through Xk. In particular, we show how to take advantage of homogeneous sets of G(those S⊆V(G)such that each vertex of V(G)\S is either adjacent to all of S or is nonadjacent to all of S) to relate the chromatic symmetric function of G to those of simpler graphs. Furthermore, we show how extending this idea to homogeneous pairs S1 S2 ⊆ V(G) generalizes the process used by Guay-Paquet to reduce the Stanley-Stembridge conjecture to unit interval graphs. | en |
dc.description.sponsorship | Natural Sciences and Engineering Research Council of Canada (NSERC), RGPIN-2020-03912 || NSERC, RGPIN-2022-03093. | en |
dc.language.iso | en | en |
dc.publisher | Elsevier | en |
dc.relation.ispartofseries | Advances in Applied Mathematics;102718 | |
dc.rights | Attribution 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
dc.subject | chromatic symmetric function | en |
dc.subject | multisymmetric function | en |
dc.subject | symmetric function | en |
dc.subject | deletion-contraction | en |
dc.subject | structural graph theory | en |
dc.subject | Stanley-Stembridge conjecture | en |
dc.title | Homogeneous sets in graphs and a chromatic multisymmetric function | en |
dc.type | Article | en |
dcterms.bibliographicCitation | Crew, L., Haithcock, E., Reynes, J., & Spirkl, S. (2024). Homogeneous sets in graphs and a chromatic multisymmetric function. Advances in Applied Mathematics, 158, 102718. https://doi.org/10.1016/j.aam.2024.102718 | en |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.contributor.affiliation2 | Combinatorics and Optimization | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Reviewed | en |
uws.scholarLevel | Faculty | en |