A cancellation-free antipode formula (for uniform matroids) for the restriction-contraction matroid Hopf algebra
arXiv:1612.04343
Abstract
In this paper, we give a cancellation-free antipode formula (for uniform matroids) for the restriction-contraction matroid Hopf algebra, using the technique of splitting and merging via a sign-reversing involution. The cancellation-free formula expresses the antipode of uniform matroids as a sum over certain ordered set partitions.
14 pages. Added some references in v2. Added some corrections in v3. Comments welcome!