Surveys In Combinatorics 2024
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Surveys In Combinatorics 2024
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Author : Felix Fischer
language : en
Publisher: Cambridge University Press
Release Date : 2024-06-13
Surveys In Combinatorics 2024 written by Felix Fischer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-13 with Mathematics categories.
This volume contains surveys of current research directions in combinatorics written by leading researchers in their fields.
Advancing Uncertain Combinatorics Through Graphization Hyperization And Uncertainization Fuzzy Neutrosophic Soft Rough And Beyond
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-20
Advancing Uncertain Combinatorics Through Graphization Hyperization And Uncertainization Fuzzy Neutrosophic Soft Rough And Beyond written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-20 with Mathematics categories.
This book is the fifth volume in the series of Collected Papers on Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond. This volume specifically delves into the concept of Various SuperHyperConcepts, building on the foundational advancements introduced in previous volumes. The series aims to explore the ongoing evolution of uncertain combinatorics through innovative methodologies such as graphization, hyperization, and uncertainization. These approaches integrate and extend core concepts from fuzzy, neutrosophic, soft, and rough set theories, providing robust frameworks to model and analyze the inherent complexity of real-world uncertainties. At the heart of this series lies combinatorics and set theory—cornerstones of mathematics that address the study of counting, arrangements, and the relationships between collections under defined rules. Traditionally, combinatorics has excelled in solving problems involving uncertainty, while advancements in set theory have expanded its scope to include powerful constructs like fuzzy and neutrosophic sets. These advanced sets bring new dimensions to uncertainty modeling by capturing not just binary truth but also indeterminacy and falsity. In this fifth volume, the exploration of Various SuperHyperConcepts provides an innovative lens to address uncertainty, complexity, and hierarchical relationships. It synthesizes key methodologies introduced in earlier volumes, such as hyperization and neutrosophic extensions, while advancing new theories and applications. From pioneering hyperstructures to applications in advanced decision-making, language modeling, and neural networks, this book represents a significant leap forward in uncertain combinatorics and its practical implications across disciplines. The book is structured into 17 chapters, each contributing unique perspectives and advancements in the realm of Various SuperHyperConcepts and their related frameworks: Chapter 1 introduces the concept of Body-Mind-Soul-Spirit Fluidity within psychology and phenomenology, while examining established social science frameworks like PDCA and DMAIC. It extends these frameworks using Neutrosophic Sets, a flexible extension of Fuzzy Sets, to improve their adaptability for mathematical and programming applications. The chapter emphasizes the potential of Neutrosophic theory to address multi-dimensional challenges in social sciences. Chapter 2 delves into the theoretical foundation of Hyperfunctions and their generalizations, such as Hyperrandomness and Hyperdecision-Making. It explores higher-order frameworks like Weak Hyperstructures, Hypergraphs, and Cognitive Hypermaps, aiming to establish their versatility in addressing multi-layered problems and setting a foundation for further studies. Chapter 3 extends traditional decision-making methodologies into HyperDecision-Making and n-SuperHyperDecision-Making. By building on approaches like MCDM and TOPSIS, this chapter develops frameworks capable of addressing complex decision-making scenarios, emphasizing their applicability in dynamic, multi-objective contexts. Chapter 4 explores integrating uncertainty frameworks, including Fuzzy, Neutrosophic, and Plithogenic Sets, into Large Language Models (LLMs). It proposes innovative models like Large Uncertain Language Models and Natural Uncertain Language Processing, integrating hierarchical and generalized structures to advance the handling of uncertainty in linguistic representation and processing. Chapter 5 introduces the Natural n-Superhyper Plithogenic Language by synthesizing natural language, plithogenic frameworks, and superhyperstructures. This innovative construct seeks to address challenges in advanced linguistic and structural modeling, blending attributes of uncertainty, complexity, and hierarchical abstraction. Chapter 6 defines mathematical extensions such as NeutroHyperstructures and AntiHyperstructures using the Neutrosophic Triplet framework. It formalizes structures like neutro-superhyperstructures, advancing classical frameworks into higher-dimensional realms. Chapter 7 explores the extension of Binary Code, Gray Code, and Floorplans through hyperstructures and superhyperstructures. It highlights their iterative and hierarchical applications, demonstrating their adaptability for complex data encoding and geometric arrangement challenges. Chapter 8 investigates the Neutrosophic TwoFold SuperhyperAlgebra, combining classical algebraic operations with neutrosophic components. This chapter expands upon existing algebraic structures like Hyperalgebra and AntiAlgebra, exploring hybrid frameworks for advanced mathematical modeling. Chapter 9 introduces Hyper Z-Numbers and SuperHyper Z-Numbers by extending the traditional Z-Number framework with hyperstructures. These extensions aim to represent uncertain information in more complex and multidimensional contexts. Chapter 10 revisits category theory through the lens of hypercategories and superhypercategories. By incorporating hierarchical and iterative abstractions, this chapter extends the foundational principles of category theory to more complex and layered structures. Chapter 11 formalizes the concept of n-SuperHyperBranch-width and its theoretical properties. By extending hypergraphs into superhypergraphs, the chapter explores recursive structures and their potential for representing intricate hierarchical relationships. Chapter 12 examines superhyperstructures of partitions, integrals, and spaces, proposing a framework for advancing mathematical abstraction. It highlights the potential applications of these generalizations in addressing hierarchical and multi-layered problems. Chapter 13 revisits Rough, HyperRough, and SuperHyperRough Sets, introducing new concepts like Tree-HyperRough Sets. The chapter connects these frameworks to advanced approaches for modeling uncertainty and complex relationships. Chapter 14 explores Plithogenic SuperHyperStructures and their applications in decision-making, control, and neuro systems. By integrating these advanced frameworks, the chapter proposes innovative directions for extending existing systems to handle multi-attribute and contradictory properties. Chapter 15 focuses on superhypergraphs, expanding hypergraph concepts to model complex structural types like arboreal and molecular superhypergraphs. It introduces Generalized n-th Powersets as a unifying framework for broader mathematical applications, while also touching on hyperlanguage processing. Chapter 16 defines NeutroHypergeometry and AntiHypergeometry as extensions of classical geometric structures. Using the Geometric Neutrosophic Triplet, the chapter demonstrates the flexibility of these frameworks in representing multi-dimensional and uncertain relationships. Chapter 17 establishes the theoretical groundwork for SuperHyperGraph Neural Networks and Plithogenic Graph Neural Networks. By integrating advanced graph structures, this chapter opens pathways for applying neural networks to more intricate and uncertain data representations.
Some Types Of Hyperneutrosophic Set 2 Complex Single Valued Triangular Fermatean And Linguistic Sets
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01
Some Types Of Hyperneutrosophic Set 2 Complex Single Valued Triangular Fermatean And Linguistic Sets written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Mathematics categories.
This paper is a continuation of the work presented in [35]. The Neutrosophic Set provides a mathematical framework for managing uncertainty, characterized by three membership functions: truth, indeterminacy, and falsity. Recent advancements have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to address more complex and multidimensional challenges. In this study, we extend the Complex Neutrosophic Set, Single-Valued Triangular Neutrosophic Set, Fermatean Neutrosophic Set, and Linguistic Neutrosophic Set within the frameworks of Hyperneutrosophic Sets and SuperHyperneutrosophic Sets. Furthermore, we investigate their mathematical structures and analyze their connections with other set-theoretic concepts.
Surveys In Combinatorics 2013
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Author : Simon R. Blackburn
language : en
Publisher: Cambridge University Press
Release Date : 2013-06-27
Surveys In Combinatorics 2013 written by Simon R. Blackburn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-27 with Mathematics categories.
This volume contains nine survey articles based on the invited lectures given at the 24th British Combinatorial Conference, held at Royal Holloway, University of London in July 2013. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, matroid theory and automatic counting, as well as connections to coding theory and Bent functions. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of cutting-edge developments. The book provides a valuable survey of the present state of knowledge in combinatorics, and will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics.
Open Problems In Algebraic Combinatorics
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Author : Christine Berkesch
language : en
Publisher: American Mathematical Society
Release Date : 2024-08-21
Open Problems In Algebraic Combinatorics written by Christine Berkesch and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-21 with Mathematics categories.
In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
A Concise Study Of Some Superhypergraph Classes
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-15
A Concise Study Of Some Superhypergraph Classes written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-15 with Mathematics categories.
In graph theory, the hypergraph [22] extends the traditional graph structure by allowing edges to connect multiple vertices, and this concept is further broadened by the superhypergraph [174,176]. Additionally, several types of uncertain graphs have been explored, including fuzzy graphs [136, 153], neutrosophic graphs [35, 36], and plithogenic graphs [66, 75, 185]. This study explores the SuperHyperGraph, Single-Valued Neutrosophic Quasi SuperHyperGraph, and Plithogenic Quasi SuperHyperGraph, analyzing their relationships with other graph classes. Future work will define the Semi Superhypergraph, Multi Superhypergraph, Pseudo Superhypergraph, Mixed Superhypergraph, and Bidirected Superhypergraph and examine their connections to existing classes in hypergraphs and graphs.
Surveys In Combinatorics 1991
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Author : A. D. Keedwell
language : en
Publisher: Cambridge University Press
Release Date : 1991
Surveys In Combinatorics 1991 written by A. D. Keedwell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This volume contains the invited papers presented at the British Combinatorial Conference, held at the University of Surrey in July 1991. As in previous years, the speakers were mathematicians of the highest quality who spanned the subject area, and their papers will provide excellent reading for all those interested in combinatorics.
Some Types Of Hyperneutrosophic Set 3 Dynamic Quadripartitioned Pentapartitioned Heptapartitioned M Polar
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Author :
language : en
Publisher: Infinite Study
Release Date : 2025-01-01
Some Types Of Hyperneutrosophic Set 3 Dynamic Quadripartitioned Pentapartitioned Heptapartitioned M Polar written by and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Mathematics categories.
This paper builds upon the foundation established in [50, 51]. The Neutrosophic Set provides a robust mathematical framework for handling uncertainty, defined by three membership functions: truth, indeterminacy, and falsity. Recent developments have introduced extensions such as the Hyperneutrosophic Set and SuperHyperneutrosophic Set to tackle increasingly complex and multidimensional problems. In this study, we explore further extensions, including the Dynamic Neutrosophic Set, Quadripartitioned Neutrosophic Set, Pentapartitioned Neutrosophic Set, Heptapartitioned Neutrosophic Set, and m-Polar Neutrosophic Set, to address advanced challenges and applications.
Survey Of Planar And Outerplanar Graphs In Fuzzy And Neutrosophic Graphs
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Author : Takaaki Fujita
language : en
Publisher: Infinite Study
Release Date : 2025-01-01
Survey Of Planar And Outerplanar Graphs In Fuzzy And Neutrosophic Graphs written by Takaaki Fujita and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-01 with Mathematics categories.
As many readers may know, graph theory is a fundamental branch of mathematics that explores networks made up of nodes and edges, focusing on their paths, structures, and properties [196]. A planar graph is one that can be drawn on a plane without any edges intersecting, ensuring planarity. Outerplanar graphs, a subset of planar graphs, have all their vertices located on the boundary of the outer face in their planar embedding. In recent years, outerplanar graphs have been formally defined within the context of fuzzy graphs. To capture uncertain parameters and concepts, various graphs such as fuzzy, neutrosophic, Turiyam, and plithogenic graphs have been studied. In this paper, we investigate planar graphs, outerplanar graphs, apex graphs, and others within the frameworks of neutrosophic graphs, Turiyam Neutrosophic graphs, fuzzy graphs, and plithogenic graphs.
Strongly Regular Graphs
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Author : Andries E. Brouwer
language : en
Publisher:
Release Date : 2022-01-13
Strongly Regular Graphs written by Andries E. Brouwer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-13 with Language Arts & Disciplines categories.
This monograph on strongly regular graphs is an invaluable reference for anybody working in algebraic combinatorics.