Enumeration of Rosenberg hypergroups

Cristea, Irina; Jafarpour, M.; Mousavi, S. Sh.; Soleymani, A.

doi:10.1016/j.camwa.2010.09.027

Cited by 11 publications

(3 citation statements)

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“…The enumeration of hypercompositional structures is the subject of several papers (e.g., [78][79][80][81][82][83][84][85][86][87]). In [78] a symbolic manipulation package is developed which enumerates the hypergroups of order 3, separates them into isomorphism classes and calculates their cardinality.…”

Section: Enumeration and Structure Resultsmentioning

confidence: 99%

On the Theory of Left/Right Almost Groups and Hypergroups with their Relevant Enumerations

Massouros

Yaqoob

2021

Mathematics

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This paper presents the study of algebraic structures equipped with the inverted associativity axiom. Initially, the definition of the left and the right almost-groups is introduced and afterwards, the study is focused on the more general structures, which are the left and the right almost-hypergroups and on their enumeration in the cases of order 2 and 3. The outcomes of these enumerations compared with the corresponding in the hypergroups reveal interesting results. Next, fundamental properties of the left and right almost-hypergroups are proved. Subsequently, the almost hypergroups are enriched with more axioms, like the transposition axiom and the weak commutativity. This creates new hypercompositional structures, such as the transposition left/right almost-hypergroups, the left/right almost commutative hypergroups, the join left/right almost hypergroups, etc. The algebraic properties of these new structures are analyzed and studied as well. Especially, the existence of neutral elements leads to the separation of their elements into attractive and non-attractive ones. If the existence of the neutral element is accompanied with the existence of symmetric elements as well, then the fortified transposition left/right almost-hypergroups and the transposition polysymmetrical left/right almost-hypergroups come into being.

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Section: Enumeration and Structure Resultsmentioning

confidence: 99%

On the Theory of Left/Right Almost Groups and Hypergroups with their Relevant Enumerations

Massouros

Yaqoob

2021

Mathematics

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“…However, issues pertaining to the enumeration of hypercompositional structures are of special interest [e.g. 3,4,5,20,31,32]. In the following paragraph we will deal with the enumeration of a class of hypercompositional structures that satisfy the transposition axiom.…”

Section: Introductionmentioning

confidence: 99%

On the enumeration of rigid hypercompositional structures

Massouros¹

2015

AIP Conference Proceedings

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“…[5] We say that two partial hypergroupoids (H, • 1 ) and (H, • 2 ) are weak mutually associative or w.m.a., if for all (x, y, z) ∈ H 3 , we have: …”

Section: Derived Non-strongly Associative Hypergroups From Groupsmentioning

confidence: 99%