On the Hopf superalgebra of symmetric functions in superspace

Abstract We introduce a superspace analogue of combinatorial Hopf algebras (Aguiar–Bergeron–Sottile, Compos. Math. 142 (2006), 1–30), and show that the Hopf superalgebra of quasi‐symmetric (resp., symmetric) functions in superspace (Fishel–Lapointe–Pinto, J. Combin. Theory Ser. A 166 (2019), 144–170) 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, Adv. Math. 111 (1995), 166–194) using the chromatic Hopf superalgebra of two‐colored graphs.