On some combinatorial aspects of transposition n-ary hypergroups
The aim of this research work is to define and characterize a new class of algebraic hyperstructures that we call weak transposition n-ary hypergroups. They are a generalization of transposition hypergroups, n-ary polygroups and join n-spaces. A subclass of weak transposition n-ary hypergroups is studied. Also, we prove that the class of weak transposition n-ary hypergroups with a unique scalar identity and the class of n-ary polygroups coincide.