Advanced results in enumeration of hyperfields

Ameri, R.; Eyvazi, M.; Hošková-Mayerová, Šárka

doi:10.3934/math.2020422

Cited by 5 publications

(11 citation statements)

References 7 publications

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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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Section: Classification Of Finite Hyperfields Into Quotient and Non-q...mentioning

confidence: 99%

“…The enumeration of certain finite hyperfields has been conducted in several papers [66,71,73,77]. Paper [66] deals with hyperfields of order less than or equal to 4, [73,77] deals with hyperfields of order less than or equal to 5, and [71] deals with hyperfields of order less than or equal to 6. In [71], R. Ameri, M. Eyvazi, and S. Hoskova-Mayerova make a thorough check of the isomorphism of these hyperfields to the quotient hyperfields using conclusions from the papers [46][47][48][95][96][97].…”

Section: Classification Of Finite Hyperfields Into Quotient and Non-q...mentioning

confidence: 99%

“…Paper [66] deals with hyperfields of order less than or equal to 4, [73,77] deals with hyperfields of order less than or equal to 5, and [71] deals with hyperfields of order less than or equal to 6. In [71], R. Ameri, M. Eyvazi, and S. Hoskova-Mayerova make a thorough check of the isomorphism of these hyperfields to the quotient hyperfields using conclusions from the papers [46][47][48][95][96][97]. This section addresses the isomorphism problems with the use of the techniques which were developed from the above study, while it covers some of the gaps that appear in [71].…”

Section: Classification Of Finite Hyperfields Into Quotient and Non-q...mentioning

confidence: 99%

“…In [71], R. Ameri, M. Eyvazi, and S. Hoskova-Mayerova make a thorough check of the isomorphism of these hyperfields to the quotient hyperfields using conclusions from the papers [46][47][48][95][96][97]. This section addresses the isomorphism problems with the use of the techniques which were developed from the above study, while it covers some of the gaps that appear in [71].…”

Section: Classification Of Finite Hyperfields Into Quotient and Non-q...mentioning

confidence: 99%

See 2 more Smart Citations

Hypergroup Theory and Algebrization of Incidence Structures

2023

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On neutro-Hv-semigroups

Mirvakili

Smarandache

Rezaei

2022

IFS

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In this paper, we extend the notion of Hv-semigroups to neutro-Hv-semigroups and anti-Hv-semigroups and investigate many of their properties. We show that these new concepts are different from the classical concept of Hv-semigroups by presenting several examples. In general, the neutro-algebras and anti-algebras are generalizations and alternatives of classical algebras. The goal and benefits of our proposed extension of this study is to explore not only the hyperoperations and axioms that are totally true as in previous algebraic hyperstructures, but also the cases when they have degrees of truth, indeterminacy and falsehood. Therefore, we enlarge the field of research.

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Advanced results in enumeration of hyperfields

Cited by 5 publications

References 7 publications

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

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

Hypergroup Theory and Algebrization of Incidence Structures

On neutro-Hv-semigroups

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