Enumeration of 3- and 4-hypergroups on sets with two elements

In this paper we classify all 3- and 4-hypergroups over sets with two elements. n-hypergroups are a natural extension of n-groups and were introduced by B. Davvaz and T. Vougiouklis in 2006. Till now, no exact statistics of n-hypergroups have been done. Moreover, there is no classification of n-groups even over small sets. That is why we use a computer program that can check and classify all n-structures over sets with two elements for n=3 and 4.