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arXiv · 1811.01687

Matroid-minor Hopf algebra: a cancellation-free antipode formula and other applications of sign-reversing involutions

Eric Bucher·Chris Eppolito·Jaiung Jun·Jacob P. Matherne
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Abstract

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.

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Eric Bucher, Chris Eppolito, Jaiung Jun, Jacob P. Matherne. 2018-11-05. Matroid-minor Hopf algebra: a cancellation-free antipode formula and other applications of sign-reversing involutions. https://arxiv.org/abs/1811.01687

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