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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.

preprint2014arXivOpen access
Erkko Lehtonen
math.CO
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Erkko Lehtonen

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