Celebrating Loday’s associahedron

Celebrating Loday’s associahedron

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 an...

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Veröffentlicht in:Archiv der Mathematik 2023-11, Vol.121 (5-6), p.559-601
Hauptverfasser: Pilaud, Vincent, Santos, Francisco, Ziegler, Günter M.
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Combinatorics
Congruences
Mathematics
Mathematics and Statistics
Metric Geometry
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Beschreibung
Zusammenfassung: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.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-023-01895-6