Strong Hypergroups of Order Three

نویسنده

  • N. J. WILDBERGER
چکیده

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 [5, 5 1 16 ] where there are two components. For weight equal to 5 the second component degenerates to a single point, the Golden hypergroup.

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تاریخ انتشار 2004