Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings
Combinatorics
2016-11-22 v2
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.
Cite
@article{arxiv.1302.7109,
title = {Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings},
author = {Erkko Lehtonen},
journal= {arXiv preprint arXiv:1302.7109},
year = {2016}
}
Comments
18 pages. Int. J. Algebra Comput. (2014)