## Associahedra, Tamari Lattices and Related Structures: Tamari Memorial FestschriftFolkert Müller-Hoissen, Jean Marcel Pallo, Jim Stasheff 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

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 |