Representations of hypergroups by generalized permutations

Special classes of generalized permutations are introduced and studied. An interpretation of them is given and they are used to represent finite hypergroups.Presented by I. Rosenberg.     

Invariant means on double coset spaces

In this paper we study invariant means on and amenability of double coset spaces. We prove the amenability of Gelfand pairs. As an application we prove a stability theorem for a functional equation related to spherical functions.     

Hypergraphs and hypergroups

We associate to every hypergraph a commutative quasi-hypergroupH _qG and find a necessary and sufficient condition on so thatH is associative. For certain, any finite included, we determine a sequence= ₀, ₁,, _n of hypergraphs such that ifH ₀ ,H ₁ ,H, H _n is the sequence of the associated quasi-hypergroups,H _n is a join space.Presented by I. Rosenberg.     

On the γ n -complete hypergroups and K H hypergroups

The class of γn-complete hypergroups is introduced. Several properties and examples are found both of γn-complete hypergroups and of KH hypergroups.     

Discrete transformation hypergroups and transformation hypergroups with phase tolerance space

Tolerance spaces and algebraic structures with compatible tolerances play an important role in contemporary algebra and its applications. In this contribution we present transformation hyperstructures, namely semihypergroups and hypergroups, acting on tolerance spaces. Some basic concepts concerning the mentioned structures are introduced and their fundamental properties are examined on suitable constructions.     

Non-Gaussian analysis and hypergroups

NANU Mathematical Institute, Kiev, Ukraine and MCS University, Lublin, Poland; NANU Mathematical Institute, Kiev, Ukraine and Bielefeld University, Germany. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 3, pp. 51–55, July–September, 1995.     

Association schemes and hypergroups

In this paper, we investigate hypergroups which arise from association schemes in a canonical way; this class of hypergroups is called realizable. We first study basic algebraic properties of realizable hypergroups. Then we prove that two interesting classes of hypergroups (partition hypergroups and linearly ordered hypergroups) are realizable. Along the way, we prove that a certain class of projective geometries is equipped with a canonical association scheme structure which allows us to link three objects; association schemes, hypergroups, and projective geometries (see, Section 1.2 for details).     

Irreducible induced representations of ICC-groups

This is an abbreviated version of a part of the author's doctorate thesis accepted by the Fakultät für Mathematik und Informatik der Technischen Universität München on 26 January 1990     

Binary relations and reduced hypergroups

Different partial hypergroupoids are associated with binary relations defined on a set H. In this paper we find sufficient and necessary conditions for these hypergroupoids in order to be reduced hypergroups. Given two binary relations ρ and σ on H we investigate when the hypergroups associated with the relations ρ∩σ, ρ∪σ and ρσ are reduced. We also determine when the cartesian product of two hypergroupoids associated with a binary relation is a reduced hypergroup.     

On the construction of hypergroups

We give a method for construction of finite, abelian hypergroups of matrices which, while including most previously known cases, also gives rise to a new family of hypergroups.     

On the construction of hypergroups

We give a method for construction of finite, abelian hypergroups of matrices which, while including most previously known cases, also gives rise to a new family of hypergroups.     

Strong local homogeneity and coset spaces

We prove that for every homogeneous and strongly locally homogeneous separable metrizable space there is a metrizable compactification of such that, among other things, for all there is a homeomorphism such that . This implies that is a coset space of some separable metrizable topological group .