Associahedra Tamari Lattices And Related Structures
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Associahedra Tamari Lattices And Related Structures
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Author : Folkert Müller-Hoissen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-13
Associahedra Tamari Lattices And Related Structures written by Folkert Müller-Hoissen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-13 with Mathematics categories.
Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This has been the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers in mathematics and mathematical physics and are accompanied by high quality illustrations.
Associahedra Tamari Lattices And Related Structures
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Author : Folkert Müller-Hoissen
language : en
Publisher: Birkhäuser
Release Date : 2012-07-13
Associahedra Tamari Lattices And Related Structures written by Folkert Müller-Hoissen and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-13 with Mathematics categories.
Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This has been the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers in mathematics and mathematical physics and are accompanied by high quality illustrations.
Mathematical Music Theory Algebraic Geometric Combinatorial Topological And Applied Approaches To Understanding Musical Phenomena
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Author : Mariana Montiel
language : en
Publisher: World Scientific Publishing
Release Date : 2018-11-08
Mathematical Music Theory Algebraic Geometric Combinatorial Topological And Applied Approaches To Understanding Musical Phenomena written by Mariana Montiel and has been published by World Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-08 with Technology & Engineering categories.
Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.
Non Kissing Complexes And Tau Tilting For Gentle Algebras
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Author : Yann Palu
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-30
Non Kissing Complexes And Tau Tilting For Gentle Algebras written by Yann Palu 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 2021-12-30 with Mathematics categories.
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Lattice Theory Special Topics And Applications
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Author : George Grätzer
language : en
Publisher: Birkhäuser
Release Date : 2016-10-08
Lattice Theory Special Topics And Applications written by George Grätzer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-08 with Mathematics categories.
George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.
Organized Time
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Author : Jason Yust
language : en
Publisher: Oxford University Press
Release Date : 2018
Organized Time written by Jason Yust and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Music categories.
Organized Time is the first attempt to unite theories of harmony, rhythm, and form under a common idea of structured time. This is a major advance in the field of music theory, leading to new theoretical approaches to topics such as closure, hypermeter, and formal function.
Recent Advances In Diffeologies And Their Applications
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Author : Jean-Pierre Magnot
language : en
Publisher: American Mathematical Society
Release Date : 2024-02-02
Recent Advances In Diffeologies And Their Applications written by Jean-Pierre Magnot 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 2024-02-02 with Mathematics categories.
This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE. The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful.
Joachim Lambek The Interplay Of Mathematics Logic And Linguistics
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Author : Claudia Casadio
language : en
Publisher: Springer Nature
Release Date : 2021-03-20
Joachim Lambek The Interplay Of Mathematics Logic And Linguistics written by Claudia Casadio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-20 with Philosophy categories.
This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard’s linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics. This book is of interest to mathematicians, logicians, linguists, and computer scientists.
Graph Theoretic Concepts In Computer Science
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Author : Isolde Adler
language : en
Publisher: Springer Nature
Release Date : 2020-10-15
Graph Theoretic Concepts In Computer Science written by Isolde Adler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-15 with Computers categories.
This book constitutes the revised papers of the 46th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2020, held in Leeds, UK, in June 2020. The workshop was held virtually due to the COVID-19 pandemic. The 32 full papers presented in this volume were carefully reviewed and selected from 94 submissions. They cover a wide range of areas, aiming to present emerging research results and to identify and explore directions of future research of concepts on graph theory and how they can be applied to various areas in computer science.
Convexity From The Geometric Point Of View
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2024-07-14
Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.