Geodesic
The hyperrings of order 3.
Journal of integer sequences, Tome 11 (2008) no. 3
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 $H_{v}$-groups of order 2, 3 and 4, we enumerate hyperrings and $H_{v}$-rings. More precisely, we found 63 hyperrings of order 2, $875 H_{v}$-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.
Classification : 20N20
Keywords: automorphism groups, hypergroups, hyperrings, hyperstructures, hv-groups 
@article{JIS_2008__11_3_a6,
     author = {Bayon,  R. and Lygeros,  N.},
     title = {The hyperrings of order 3.},
     journal = {Journal of integer sequences},
     year = {2008},
     volume = {11},
     number = {3},
     zbl = {1152.16039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_3_a6/}
}
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Bayon,  R.; Lygeros,  N. The hyperrings of order 3.. Journal of integer sequences, Tome 11 (2008) no. 3. http://geodesic.mathdoc.fr/item/JIS_2008__11_3_a6/