Associahedra Tamari Lattices And Related Structures
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Associahedra, Tamari Lattices and Related Structures
Author: Folkert Müller-Hoissen
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-07-13
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
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
Author: Mariana Montiel
language: en
Publisher: World Scientific Publishing
Release Date: 2018-11-08
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.