Results 91 to 100 of about 324 (107)

Hypergroupoids and combinatorial structures

1992
Let \((H,\circ)\) be a finite hypergroupoid and associate to \(H\) the family of subsets of \(H\) \[ {\mathcal B} = \{x\circ y\mid (x,y) \in H^ 2\} = \{X_ 1^{(n_ 1)},\dots,X_ s^{(n_ s)}\} \] where the exponents in brackets denote the multiplicities. \((H,{\mathcal B})\) is a block design and it is called the design associated to \((H,\circ)\).
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Matroidal \(M_\lambda\)-hypergroupoids. \(\lambda\)-linear mappings and automorphisms of \(M_\lambda\)-hypergroupoids

1998
In this paper a thoroughgoing study of hypergroupoids considered by the author in a previous work [Matematiche 52, No. 2, 271-295 (1997; Zbl 0941.20071)] is done. Let \(G\) be a group, \(\lambda\in G\) and \(\cdot\colon G\times M\) be an action of \(G\) on \(M\). The aim of this paper is to investigate the hyperoperation defined on \(M\) by: \(a\cdot b=
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Fundamental relation on non-associative hypergroupoids

1999
The paper deals with the fundamental relation \(\beta^*\) defined on non-associative hypergroupoids. The relation \(\beta^*\) on classes weaker than semihypergroups is studied, in relation with axioms originating from feebly associativity and strongly regular equivalence. Examples are also provided.
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Binary relations and hypergroupoids

2000
The author associates a partial hyperoperation \(\langle\widetilde\circ_R\rangle\) to every binary relation \(R\) defined on a non-empty set \(H\) in the following way: \(x\widetilde\circ_R y=\{z\in H\mid xRz,\;zRy\}\). The hyperstructure \(\langle H,\widetilde\circ_R\rangle\) is a partial hypergroupoid and the necessary and sufficient condition so ...
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Soft crossed hypermodules and soft HG-hypergroupoids

Summary: In this article, we introduce the soft subhypergroupoid and soft action hypergroupoid and study their properties. We consider the category of soft hypergroupoids whose objects are soft hypergroupoids and morphisms are soft hypergroupoid homomorphisms.
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Hypergroupoids and fundamental relation

1994
In this work we study hypergroupoids whose β-relation is transitive, by using the fundamental relations β, β*, δ and δ*. We take several examples, finding the necessary and sufficient conditions such that a quasi-hypergroup has β*=β=δ=δ* (i.e. it is of kind T_1).
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Partial hypergroupoids of class two.

1994
The author studies the finite partial hypergroupoids, such that there are exactly two pairs of elements, which define non-empty hyperproducts. He solves the combinatorial problem of finding, up to isomorphism, the number of the aforesaid hyperstructure.
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A new class of hypergroupoids associated to binary relations.

2003
Suppose that in a set a relation is considered, then several partial hyperoperations can be defined and studied. The authors define a new hyperoperation which is `smaller' than the one they already introduced and studied. Some properties of the above hyperstructure are proved and using a computer the size of those hyperoperations is obtained.
DE SALVO, Mario, LO FARO, Giovanni
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Isomorphism classes in finite partial hypergroupoids of class two

1996
Let \(H\) be a set with \(n\) elements and \(\circ\colon H\times H\to{\mathcal P}(H)\) be a partial hyperoperation on \(H\). If the set \(\{(a,b)\in H^2\mid a\circ b\neq\emptyset\}\) has \(k\) elements, where \(k\in\{0,1,\dots,n^2\}\), then the partial hypergroupoid \((H,\circ)\) is said to be of class \(k\).
DE SALVO, Mario, LO FARO, Giovanni
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A note on the cyclic hypergroupoids

1995
In this paper one begins to studi cyclic hypergroupoids. In particular, in the finite case, by using the set C_x= \{n\in N^* | x^{(n+1)}\subseteq \bigcup_{k=1}^n x^{(k)} \} and the maximum element of the set N-C_x, one characterizes the structure of the cyclic subhypergroupoid generated by x.
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