2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118205We show that with the appropriate choice of coproduct, the type B quasisymmetric functions form a Hopf algebra, and the recently introduced type B peak functions form a Hopf subalgebra.9 pagesCombinatoricsRings and AlgebrasThe Hopf algebras of type B quasisymmetric functions and peak functionstext