Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $h^*$-vectors of graph polytopes using activities of dissecting spanning
  trees   Both for symmetric edge polytopes of graphs, and root polytopes of
semi-balanced digraphs, there is a large, natural class of dissections into
simplices: these are dissections where the simplices correspond to certain
(oriented) spanning trees. We show that for any "spanning tree dissection" of
the symmetric edge polytope of a graph, or the root polytope of a semi-balanced
digraph, the $h^*$-vector can be computed as a generating function of certain
activities of the corresponding spanning trees. This also implies that the
distribution of both these activity statistics is independent of the dissection
and other auxiliary data.

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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph