[HTML][HTML] Antipodes and involutions
C Benedetti, BE Sagan - Journal of Combinatorial Theory, Series A, 2017 - Elsevier
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 …
its antipode. However, there is usually massive cancellation in the result. We show how sign …
Universal Tutte characters via combinatorial coalgebras
This work discusses the extraction of meaningful invariants of combinatorial objects from
coalgebra or bialgebra structures. The Tutte polynomial is an invariant of graphs well known …
coalgebra or bialgebra structures. The Tutte polynomial is an invariant of graphs well known …
Matroid-minor Hopf algebra: a cancellation-free antipode formula and other applications of sign-reversing involutions
E Bucher, C Eppolito, J Jun, JP Matherne - arXiv preprint arXiv …, 2018 - arxiv.org
In this paper, we give a cancellation-free antipode formula for the matroid-minor Hopf
algebra. We then explore applications of this formula. For example, the cancellation-free …
algebra. We then explore applications of this formula. For example, the cancellation-free …