Journal of Integer Sequences, Vol. 11 (2008), Article 08.3.2

The Hyperrings of Order 3

R. Bayon
14 av. du bosquet
06160 Juan les Pins

N. Lygeros
14 av. Condorcet
69100 Villeurbanne


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.

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(Concerned with sequences A108089 A132590 and A132591.)

Received September 9 2007; revised version received July 25 2008. Published in Journal of Integer Sequences, August 1 2008.

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