Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matroid-minor Hopf algebra: a cancellation-free antipode formula and
  other applications of sign-reversing involutions   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.

36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat