Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic matroids and Frobenius flocks   We show that each algebraic representation of a matroid $M$ in positive
characteristic determines a matroid valuation of $M$, which we have named the
{\em Lindstr\"om valuation}. If this valuation is trivial, then a linear
representation of $M$ in characteristic $p$ can be derived from the algebraic
representation. Thus, so-called rigid matroids, which only admit trivial
valuations, are algebraic in positive characteristic $p$ if and only if they
are linear in characteristic $p$.
  To construct the Lindstr\"om valuation, we introduce new matroid
representations called flocks, and show that each algebraic representation of a
matroid induces flock representations.

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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc