Strong hypergroups of order three

This paper investigates the question of when a finite hypergroup with three elements is strong, that is satisfies the condition that its dual signed hypergroup is actually a hypergroup. We classify hermitian hypergroups of order three by weight into two-dimensional families and show that the algebraic conditions arising from duality yield four interesting curves in the plane which bound the character values of strong and non-strong hypergroups. By analysing the relations between these curves we discover that the stratum of strong hypergroups is connected for all weights in the range [4,∞) except for the subinterval image where there are two components. For weight equal to 5 the second component degenerates to a single point, the Golden hypergroup.