Associahedra, Tamari Lattices and Related Structures: Tamari Memorial Festschrift

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Folkert Müller-Hoissen, Jean Marcel Pallo, Jim Stasheff
Springer Science & Business Media, Jul 13, 2012 - Mathematics - 436 pages
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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.

 

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Contents

Dov Tamari formerly Bernhard Teitler
1
On Being a Student of Dov Tamari
41
How I met Dov Tamari
45
Dichotomy of the Addition of Natural Numbers
65
Partial Groupoid Embeddings in Semigroups
81
Moduli Spaces of Punctured Poincaré Disks
99
Realizing the Associahedron Mysteries and Questions
119
Permutahedra and Associahedra
129
Parenthetic Remarks
251
On the Categories of Modules Over the Tamari Posets
269
The Tamari Lattice as it Arises in Quiver Representations
281
From the Tamari Lattice to Cambrian Lattices and Beyond
293
Catalan Lattices on Series Parallel Interval Orders
323
Generalized Tamari Order
339
A Survey of the Higher StasheffTamari Orders
351
KP Solitons Higher Bruhat and Tamari Orders
391

Combinatorial 2truncated Cubes and Applications
161
Extending the Tamari Lattice to Some Compositions of Species
187
Tamari Lattices and the Symmetric Thompson Monoid
211
Appendix Dov Tamaris Publications
424
Index
429
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