Explicit product formulas are obtained for families of multivariate polynomials which are orthogonal on simplices and on a parabolic biangle in R. These product formulas are shown to give rise to measure algebras which are hypergroups. The article also includes an elementary proof that the Michael topology for the space of compact subsets of a topological space (which is used in the definition ...

Starting with the underlying motivation of developing a general theory of L-fuzzy sets where L is a multilattice (a particular case of non-deterministic algebra), we study the relationship between the crisp notions of congruence, homomorphism and substructure on some non-deterministic algebras which have been used in the literature, i.e. hypergroups, and join spaces. Moreover, we provide suitab...

in this paper we define ?-independent (a weak-version of independence), kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and sidon sets. these sets have the lacunarity or thinness property and are very useful indeed. for example varopoulos used the kronecker sets to prove the malliavin theorem. in t...

applications of hypergroups have mainly appeared in special subclasses. one of the important subclasses is the class of polygroups. in this paper, we study the notions of nilpotent and solvable polygroups by using the notion of heart of polygroups. in particular, we give a necessary and sufficient condition between nilpotent (solvable) polygroups and fundamental groups.

In this paper we introduce the smallest equivalence relation ξ∗ on a finite fuzzy hypergroup S such that the quotient group S/ξ∗, the set of all equivalence classes, is a solvable group. The characterization of solvable groups via strongly regular relation is investigated and several results on the topic are presented.

In this paper, we present some connections between tree automaton theory and hyperstructure theory. In this regard, at first we construct some hyperoperations on the set of trees and, specially, prove that one of them creates a join space. Also, we define a hyperoperation on the states of a tree automaton and, based on the properties of the tree automaton, we show that the proposed hyperoperati...