Reference : Reconstructing multisets over commutative groupoids and affine functions over nonasso...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/16045
Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings
English
Lehtonen, Erkko mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
2014
International Journal of Algebra and Computation
World Scientific Publishing Company
24
1
11-31
Yes (verified by ORBilu)
International
0218-1967
1793-6500
[en] reconstruction problem ; multiset ; function of several arguments ; commutative groupoid ; semiring
[en] 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.
http://hdl.handle.net/10993/16045
10.1142/S0218196714500027
http://www.worldscientific.com/worldscinet/ijac
Preprint of an article published in International Journal of Algebra and Computation (2014), DOI: 10.1142/S0218196714500027. © copyright World Scientific Publishing Company. http://www.worldscientific.com/worldscinet/ijac

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