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arXiv · 1302.7109

Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings

Erkko Lehtonen
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Abstract

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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Erkko Lehtonen. 2014-03-15. Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings. https://doi.org/10.1142/s0218196714500027

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