On the Hopf superalgebra of symmetric functions in superspace
arXiv:2412.17670 · doi:10.1112/blms.70183
Abstract
We introduce a superspace analogue of combinatorial Hopf algebras (Aguiar-Bergeron-Sottile, 2006), and show that the Hopf superalgebra of quasi-symmetric (resp. symmetric) functions in superspace (Fishel-Lapointe-Pinto, 2019) is a terminal object in the category of all (resp. cocommutative) combinatorial Hopf superalgebras. We also introduce a superspace analogue of chromatic symmetric functions of graphs (Stanley, 1995) using the chromatic Hopf superalgebra of two-colored graphs.
14 pages,the manuscript that has been accepted for the publication in the Bulletin of the London Mathematical Society