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- Title
RECONSTRUCTING MULTISETS OVER COMMUTATIVE GROUPOIDS AND AFFINE FUNCTIONS OVER NON ASSOCIATIVE SEMIRINGS.
- Authors
LEHTONEN, ERKKO
- 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. Nec-essary and sufficient conditions for the reconstructibility of multisets are determined. These results find an application in a different kind of reconstruction problem for func-tions 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.
- Subjects
SET theory; MATHEMATICAL functions; NONASSOCIATIVE rings; GROUPOIDS; ABELIAN groups
- Publication
International Journal of Algebra & Computation, 2014, Vol 24, Issue 1, p11
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196714500027