[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 …

Universal Tutte characters via combinatorial coalgebras

C Dupont, A Fink, L Moci - Algebraic Combinatorics, 2018 - alco.centre-mersenne.org
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 …

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 …

[引用][C] Research Statement: Combinatorial Methods in Algebra and Geometry