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Associahedra, Tamari Lattices and Related Structures

Tamari Memorial Festschrift

  • Book
  • © 2012

Overview

Editors:
  1. Folkert Müller-Hoissen

    1. for Dynamics and Self-Organization, Max-Planck-Institute, Göttingen, Germany

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  2. Jean Marcel Pallo

    1. , Département d'Informatique, LE2I, Université de Bourgogne, Dijon Cedex, France

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  3. Jim Stasheff

    1. , Department of Mathematics, University of North Carolina at Chapel H, Chapel Hill, USA

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  • First (and only) book centering around associahedra, Tamari lattices, and their generalizations, a highly multifaceted and interdisciplinary topic
  • Profusely illustrated with accessible introductions to much of current related research
  • Includes the first comprehensive biography of the mathematician Dov Tamari, based on original biographical material from various archives and other sources
  • Includes supplementary material: sn.pub/extras

Part of the book series: Progress in Mathematics (PM, volume 299)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Dov Tamari (formerly Bernhard Teitler)

    • Folkert Müller-Hoissen, Hans-Otto Walther
    Pages 1-40

  3. On Being a Student of Dov Tamari

    • Carl Maxson
    Pages 41-44

  4. How I ‘met’ Dov Tamari

    • Jim Stasheff
    Pages 45-63

  5. Dichotomy of the Addition of Natural Numbers

    • Jean-Louis Loday
    Pages 65-79

  6. Partial Groupoid Embeddings in Semigroups

    • Susan H. Gensemer
    Pages 81-97

  7. Moduli Spaces of Punctured Poincaré Disks

    • Satyan L. Devadoss, Benjamin Fehrman, Timothy Heath, Aditi Vashist
    Pages 99-117

  8. Realizing the Associahedron: Mysteries and Questions

    • Cesar Ceballos, Günter M. Ziegler
    Pages 119-127

  9. Permutahedra and Associahedra

    • Christophe Hohlweg
    Pages 129-159

  10. Combinatorial 2-truncated Cubes and Applications

    • Victor M. Buchstaber, Vadim D. Volodin
    Pages 161-186

  11. Extending the Tamari Lattice to Some Compositions of Species

    • Stefan Forcey
    Pages 187-210

  12. Tamari Lattices and the Symmetric Thompson Monoid

    • Patrick Dehornoy
    Pages 211-250

  13. Parenthetic Remarks

    • Ross Street
    Pages 251-268

  14. On the Categories of Modules Over the Tamari Posets

    • Frédéric Chapoton
    Pages 269-280

  15. The Tamari Lattice as it Arises in Quiver Representations

    • Hugh Thomas
    Pages 281-291

  16. From the Tamari Lattice to Cambrian Lattices and Beyond

    • Nathan Reading
    Pages 293-322

  17. Catalan Lattices on Series Parallel Interval Orders

    • Filippo Disanto, Luca Ferrari, Renzo Pinzani, Simone Rinaldi
    Pages 323-338

  18. Generalized Tamari Order

    • María Ronco
    Pages 339-350

  19. A Survey of the Higher Stasheff-Tamari Orders

    • Jörg Rambau, Victor Reiner
    Pages 351-390

  20. KP Solitons, Higher Bruhat and Tamari Orders

    • Aristophanes Dimakis, Folkert Müller-Hoissen
    Pages 391-423
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Keywords

About this book

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.

Editors and Affiliations

  • for Dynamics and Self-Organization, Max-Planck-Institute, Göttingen, Germany

    Folkert Müller-Hoissen

  • , Département d'Informatique, LE2I, Université de Bourgogne, Dijon Cedex, France

    Jean Marcel Pallo

  • , Department of Mathematics, University of North Carolina at Chapel H, Chapel Hill, USA

    Jim Stasheff

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