Abstract
We study some connections between hypergroups and n-hypergroups. For each of them we give examples which involve binary relations, lattices and hypergraphs. Finally, we study when two finite join spaces associated with lattices, defined on the same set, are isomorphic.
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Corsini P, Leoreanu V (2003) Applications of hyperstructure theory. Kluwer, Dordrecht
Corsini P, Leoreanu V (1995) Join spaces associated with fuzzy sets. J Comb Inf Syst Sci 20(1)
Corsini P, Leoreanu V (2000) Hypergroups and binary relations. Algebra Universalis 43: 321–330
Davvaz B (2008) Approximations in n-ary algebraic systems, Soft Computing, A Fusion of Foundations, Methodologies and Applications Issue Volume 12, Number 4
Davvaz B, Karimian M (2007) On the n-complete hypergroups. Eur J Comb 28(1): 86–93
Davvaz B, Vougiouklis T (2006) n-ary hypergroups. Iran J Sci Technol Trans A 30
Dörnte W (1928) Untersuchungen über einen verallgemeinerten Gruppenbegriff. Math Z 29: 1–19
Kerner R (2000) Ternary algebraic structures and their applications in physics. University of P M Curie, Paris
Grzymala-Busse JW (1969) Automorphisms of polyadic automata. J Assoc Comput Mach 16: 208–219
Laywine CF, Mullen GL (1998) Discrete mathematics using latin squares. Wiley, New York
Laywine CF, Mullen GL, Whittle G (1995) D-dimensional hypercubes and the Euler and MacNeish conjectures. Monatsh Math 111: 223–238
Leoreanu-Fotea V, Davvaz B (2008a) n-hypergroups and binary relations. Eur J Comb 29(5): 1207–1218
Leoreanu-Fotea V, Davvaz B (2008b) Join n-spaces and lattices. Mult Valued Logic Soft Comput (Accepted)
Marty F (1934) Sur une généralisation de la notion de groupe, IV Congrès des Mathématiciens Scandinaves, Stockholm, pp 45–49
Nikshych D, Vainerman L (2000) Finite quantum groupoids and their applications. University of California, Los Angeles
Prenowitz W, Jantosciak J (1979) Join geometries. Springer-Verlag UTM
Rosenberg IG (1998) Hypergroups and join spaces determined by relations. It J Pure Appl Math 4: 93–101
Stojaković Z, Dudek WA (1998) Single identities for varieties equivalent to quadruple systems. Discrete Math 183: 277–284
Stojaković Z, Dudek WA (2005) Conjugate invariant quasigroups. Quasigroups Relat Syst 13 (in press)
Vougiouklis T (1994) Hyperstructures and their representations, vol 115. Hadronic Press Inc., Palm Harbor
Vougiouklis T (1992) Representations of hypergroups by generalized permutations. Algebra Universalis 29: 172–183
Vougiouklis T (1996) H v -groups defined on the same set. Discrete Math 155: 259–265
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This work was supported by a Romanian Academy Grant, 2007/2008.
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Leoreanu-Fotea, V., Corsini, P. Isomorphisms of hypergroups and of n-hypergroups with applications. Soft Comput 13, 985–994 (2009). https://doi.org/10.1007/s00500-008-0341-9
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DOI: https://doi.org/10.1007/s00500-008-0341-9