In several papers I've seen on Combinatorial Hopf Algebras, the algebra and coalgebra structures are described, but no antipode is defined. CHAs generally have a natural grading, and are of finite dimension in each degree, and I have seen one comment which suggested that this leads to an obvious or unique antipode. If so, please can someone spell it out.
(Are there any good introductory papers on CHAs, as the ones I've found so far all go straight in at the deep end.)