Celebrating Loday’s associahedron

Vincent Pilaud; Francisco Santos; Günter M. Ziegler

doi:10.1007/s00013-023-01895-6

Celebrating Loday’s associahedron

Vincent Pilaud
, Francisco Santos
, Günter M. Ziegler

Research output: Contribution to journal › Article › peer-review

Abstract

We survey Jean-Louis Loday’s vertex description of the associahedron, and its far reaching influence in combinatorics, discrete geometry, and algebra. We present in particular four topics where it plays a central role: lattice congruences of the weak order and their quotientopes, cluster algebras and their generalized associahedra, nested complexes and their nestohedra, and operads and the associahedron diagonal.

Original language	English
Pages (from-to)	559-601
Number of pages	43
Journal	Archiv der Mathematik
Volume	121
Issue number	5-6
DOIs	https://doi.org/10.1007/s00013-023-01895-6
Publication status	Published - 1 Nov 2023

Keywords

Associahedron
Hopf algebras
Lattices
Operads
Polytopes

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10.1007/s00013-023-01895-6

Cite this

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title = "Celebrating Loday{\textquoteright}s associahedron",

abstract = "We survey Jean-Louis Loday{\textquoteright}s vertex description of the associahedron, and its far reaching influence in combinatorics, discrete geometry, and algebra. We present in particular four topics where it plays a central role: lattice congruences of the weak order and their quotientopes, cluster algebras and their generalized associahedra, nested complexes and their nestohedra, and operads and the associahedron diagonal.",

keywords = "Associahedron, Hopf algebras, Lattices, Operads, Polytopes",

author = "Vincent Pilaud and Francisco Santos and Ziegler, \{G{\"u}nter M.\}",

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AU - Ziegler, Günter M.

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AB - We survey Jean-Louis Loday’s vertex description of the associahedron, and its far reaching influence in combinatorics, discrete geometry, and algebra. We present in particular four topics where it plays a central role: lattice congruences of the weak order and their quotientopes, cluster algebras and their generalized associahedra, nested complexes and their nestohedra, and operads and the associahedron diagonal.

KW - Associahedron

KW - Hopf algebras

KW - Lattices

KW - Operads

KW - Polytopes

U2 - 10.1007/s00013-023-01895-6

DO - 10.1007/s00013-023-01895-6

M3 - Article

AN - SCOPUS:85175291526

SN - 0003-889X

VL - 121

SP - 559

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JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 5-6

ER -

Celebrating Loday’s associahedron

Abstract

Keywords

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