2018/11/05 by Bucher, Eric, Eppolito, Chris, Jun, Jaiung +1
#05B35 (Secondary) #16T30 (Primary) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1811.01687
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 formula expresses the antipode of uniform matroids as a sum over certain ordered set partitions. We also prove that all matroids over any hyperfield (in the sense of Baker and Bowler) have cancellation-free antipode formulas; furthermore, the cancellations in the antipode are independent of the hyperfield structure and only depend on the underlying matroid.