Directed Graphs representing isomorphism classes of C-Hypergroupoids

We investigate the relation of directed graphs and hyperstructures by virtue of the graph hyperoperation. A new class of graphs arises in this way representing isomorphism classes of C-hypergroupoids and we present the 17 such graphs that correspond to the 73 C-hypergroupoids associated with binary relations on three element sets. As it is shown they constitute an upper semilattice with respect tograph inclusion

History and new possible research directions of hyperstructures

We present a summary of the origins and current developments of the theory of algebraic hyperstructures. We also sketch some possible lines of research

The algebraic hyperstructure of elementary particles in physical theory

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. Algebraic hyperstructure theory has a multiplicity of applications to other disciplines. The main purpose of this paper is to provide examples of hyperstructures associated with elementary particles in physical theory.Comment: 13 page

EL-hyperstructures: an overview

This paper gives a current overview of theoretical background of a special class of hyperstructures constructed from quasi / partially or dered (semi) groups using a construction known as the "Ends lemma". The paper is a collection of both older and new results presented at AHA 2011

General ω-hyperstructures and certain applications of those

The aim of this paper is to investigate general hyperstructures construction of which is based on ideas of A. D. Nezhad and R. S. Hashemi. Concept of general hyperstructures considered by the above mentioned authors is generalized on the case of hyperstructures with hyperoperations of countable arity. Speci cations of treated concepts to examples from various elds of the mathematical sturctures theory are also included.

THE TRANSPOSITION AXIOM IN HYPERCOMPOSITIONAL STRUCTURES

The hypergroup (as defined by F. Marty), being a very general algebraic structure, was subsequently quickly enriched with additional axioms. One of these is the transposition axiom, the utilization of which led to the creation of join spaces (join hypergroups) and of transposition hypergroups. These hypergroups have numerous applications in geometry, formal languages, thetheory of automata and graph theory. This paper deals with transposition hypergroups. It also introduces the transposition axiom to weaker structures, which result from the hypergroup by the removal of certain axioms, thus defining the transposition hypergroupoid, the transposition semi-hypergroup and the transposition quasi-hypergroup. Finally, it presents hypercompositional structures with internal or external compositions and hypercompositions, in which the transposition axiom is valid. Such structures emerged during the study of formal languages and the theory of automata through the use of hypercompositional algebra