Associahedra, Tamari Lattices and Related Structures [electronic resource] : Tamari Memorial Festschrift /
Müller-Hoissen, Folkert.editor.
Pallo, Jean Marcel.editor.
Stasheff, Jim.editor.
Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This was 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.
Description based upon print version of record.
Associahedra, Tamari Latticesand Related Structures; Preface; Contents; List of Contributors; Dov Tamari (formerly Bernhard Teitler); 1 Germany; 2 Palestine; 3 France; 4 Tamari's thesis and beyond; 5 Israel; 6 Via Princeton to Brazil; 7 The Netherlands; 8 USA; 9 Tamari-Technion Affair; 9.1 Freudenthal's initiative; 9.2 AMS and CAFTES; 10 After retirement; 10.1 Mathematical activities; 10.2 Back to the roots; 11 Further recollections; References; On Being a Student of Dov Tamari; How I 'met' Dov Tamari; 1 Introduction/History; 1.1 The so-called Stasheff polytope; 1.2 Giving due credit
5 The integers as molecules6 Multiplication of trees; 7 Trees and polynomials; 8 Realizing the associahedron; 8.1 Tamari poset; 8.2 Associahedron and regular pentagons; 8.3 Realizations of the associahedron; 9 Associahedron and the trefoil knot; References; Partial Groupoid Embeddings in Semigroups; 1 Introduction; 2 Definitions and preliminary results; 3 Results; 4 Further results; 4.1 Embedding into a partially ordered semigroup; 4.2 Embedding into a commutative semigroup; 5 Conclusion; References; Moduli Spaces of Punctured Poincaré Disks; 1 Motivation from physics
2 Particles on the Poincaré disk3 The Fulton-McPherson compactification; 4 Group actions on screens; 5 Combinatorial results; References; Realizing the Associahedron: Mysteries and Questions; 1 Introduction; 2 Realization space; 3 Vertices on a sphere; 4 Realizing the multiassociahedron; References; Permutahedra and Associahedra; 1 Introduction; 2 Permutahedra and finite reflection groups; 2.1 Finite reflection groups; 2.2 Permutahedra as V -polytopes; 2.3 Root systems and permutahedra as H -polytopes; 2.4 Faces of permutahedra and the weak order; 2.4.1 Faces and standard parabolic subgroups
2.4.2 Edges and weak order3 Coxeter generalized associahedra; 3.1 Coxeter elements and Coxeter singletons; 3.2 Coxeter generalized associahedra as H -polytopes; 3.3 Faces and almost positive roots; 3.4 Edges and Cambrian lattices; 3.5 Isometry classes; 3.6 Integer coordinates; 4 Further developments; References; Combinatorial 2-truncated Cubes and Applications; 1 Introduction; 2 Simple polytopes; 2.1 Enumerative polynomials; 3 Class of 2-truncated cubes; 4 Smooth toric varieties over 2-truncated cubes; 5 Small covers of 2-truncated cubes; 6 Nestohedra and graph-associahedra
7 Building set as a structure
Includes bibliographical references and index.
Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This was 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.
Tamari, Dov, 1911-2006.
Convex geometry .
Discrete geometry.
Number theory.
Algebra.
Ordered algebraic structures.
Algebraic topology.
Convex and Discrete Geometry.
Number Theory.
Order, Lattices, Ordered Algebraic Structures.
Algebraic Topology.