The Hyperrings of Order 3
14 av. du bosquet
06160 Juan les Pins
14 av. Condorcet
We first explain the historical and logical relations of hyperstructures
introduced by M. Krasner and R. Rota, and generalized by T.
Vougiouklis. Then, with our new algorithm based on our previous results
on hypergroups and Hv-groups of order 2, 3 and 4, we enumerate
hyperrings and Hv-rings.
More precisely, we found 63 hyperrings of
order 2, 875 Hv-rings of order 2
and 33,277,642 hyperrings of order
3. Finally, in this new context, we study a new connection between
groups and hypergroups via the notion of duality.
Full version: pdf,
(Concerned with sequences
Received September 9 2007;
revised version received July 25 2008.
Published in Journal of Integer Sequences, August 1 2008.
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