\(H_v\)-structures associated with generalized \(P\)-hyperoperations (Q1305315)

Given a groupoid \((G,\cdot)\) and any subsets of \(G\), one can define the so-called \(P\)-hyperoperations. If two subsets of \(G\) are used, then the authors define three types of \(2P\)-hyperoperations and if three subsets of \(G\) are used, then one type of \(3P\)-hyperoperation is defined. Some results on the obtained hyperstructures are proved. Moreover, the number of the \(H_v\)-rings with the above type of hyperoperations is evaluated.