Highly Influenced

@article{Benedetti2017AntipodesAI, title={Antipodes and involutions}, author={Carolina Benedetti and Bruce E. Sagan}, journal={J. Comb. Theory, Ser. A}, year={2017}, volume={148}, pages={275-315} }

- Published 2017 in J. Comb. Theory, Ser. A
DOI:10.1016/j.jcta.2016.12.005

If H is a connected, graded Hopf algebra, then Takeuchi’s formula can be used to compute its antipode. However, there is usually massive cancellation in the result. We show how sign-reversing involutions can sometimes be used to obtain cancellationfree formulas. We apply this idea to the Hopf algebras of polynomials, graphs, and noncommutative symmetric functions.