The Generalized Cluster Complex: Refined Enumeration of Faces and Related Parking Spaces

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• ISSN: 1815-0659
• Main Authors: Douvropoulos, Theo, Josuat-Vergès, Matthieu
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212015
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Generalized Cluster Complex: Refined Enumeration of Faces and Related Parking Spaces. Theo Douvropoulos and Matthieu Josuat-Vergès. SIGMA 19 (2023), 069, 40 pages

The generalized cluster complex was introduced by Fomin and Reading as a natural extension of the Fomin-Zelevinsky cluster complex coming from finite type cluster algebras. In this work, to each face of this complex, we associate a parabolic conjugacy class of the underlying finite Coxeter group. We...