Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstructing multisets over commutative groupoids and affine functions
  over nonassociative semirings   A reconstruction problem is formulated for multisets over commutative
groupoids. The cards of a multiset are obtained by replacing a pair of its
elements by their sum. Necessary and sufficient conditions for the
reconstructibility of multisets are determined. These results find an
application in a different kind of reconstruction problem for functions of
several arguments and identification minors: classes of linear or affine
functions over nonassociative semirings are shown to be weakly reconstructible.
Moreover, affine functions of sufficiently large arity over finite fields are
reconstructible.

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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn