Cancelation free formula for the antipode of linearized Hopf monoid

Nantel Bergeron, Carolina Benedetti

Many combinatorial Hopf algebras $H$ in the literature are the functorial image of a linearized Hopf monoid $\mathbf{H}$. That is, $H=\mathcal{K}(\mathbf{H})$ or $H=\overline{\mathcal K}…