Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Set of independencies and Tutte polynomial of matroids over a domain   In this work, we study matroids over a domain and several classical
combinatorial and algebraic invariants related. We define their
Grothendieck-Tutte polynomial $T_{\mathcal{M}}(x,y)$, extending the definition
given by Fink and Moci in 2016, and we show that such polynomial has the
classical deletion-contraction property.
  Moreover, we study the set of independencies for a realizable matroid over a
domain, generalizing the definition of \emph{poset of torsions}
$Gr(\mathcal{M})$ given by the second author in 2017. This is a union of
identical simplicial posets as for (quasi-)arithmetic matroids. The new notions
harmonize naturally through the face module $N_\mathcal{M}$ of the matroid over
a domain.
  Whenever $Gr(\mathcal{M})$ is a finite poset, the Hilbert series
$N_\mathcal{M}(t)$ of its face module is a specialization of the Tutte
polynomial $T_{\mathcal{M}}(x,y)$. Further, for arrangements of codimension-one
abelian subvarities of an elliptic curve admitting complex multiplication, we
extend certain results of Bibby and we provide an algebraic interpretation of
the elliptic Tutte polynomial.

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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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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: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin