|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Parastrophically equivalent quasigroup equations||Journal:||Publications de l'Institut Mathematique||Volume:||87||Issue:||101||First page:||39||Last page:||58||Issue Date:||14-Oct-2010||Rank:||M24||ISSN:||0350-1302||DOI:||10.2298/PIM1001039K||Abstract:||
Fedir M. Sokhats'kyi recently posed four problems concerning parastrophic equivalence between generalized quasigroup functional equations. Sava Krstić in his PhD thesis established a connection between generalized quadratic quasigroup functional equations and connected cubic graphs. We use this connection to solve two of Sokhats'kyi's problems, giving also complete characterization of parastrophic cancellability of quadratic equations and reducing the problem of their classification to the problem of classification of connected cubic graphs. Further, we give formulas for the number of quadratic equations with a given number of variables. Finally, we solve all equations with two variables.
|Keywords:||Cubic graph | Parastrophic cancellability | Parastrophic equivalence | Quadratic functional equation | Quasigroup||Publisher:||Mathematical Institute of the SASA||Project:||Ministry of Science and Technology of Serbia, Grants 144013 and 144018|
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