Isomorphism classes in finite partial hypergroupoids of class two.

In this extensive paper the authors give a complete solution of the problem of finding the number of distinct partial hypergroupoids of finite size, when there are exactly two ordered pairs of elements which define nonempty hyperproducts. If the size of the hypergroupoids is n then the above number is expressed by means of a polynomial function of degree 3 in the indeterminate n . The results are obtained by proving a number of lemmas and theorems and they are presented, with a list of formulas, in three tables. Finally, using the results of a Pascal program, the authors give a conjecture on the subject.