Work

A continuous associahedron of type A

Year: 2025

Type: article

Abstract: Taking a representation-theoretic viewpoint, we construct a continuous associahedron motivated by the realization of the generalized associahedron in the physical setting. We show that our associahedron shares important properties with the generalized associahedron of type A . Our continuous associahedron is convex and manifests a cluster theory: the points which correspond to the clusters are on its boundary, and the edges that correspond to mutations are given by intersections of hyperplanes. This requires development of several methods that are continuous analogues of discrete methods. We conclude the paper by showing that there is a sequence of embeddings of type A generalized associahedra into our continuous associahedron.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-025-03864-x

Authors: Maitreyee C. Kulkarni, Jacob P. Matherne, Kaveh Mousavand, Job D. Rock

Institutions: North Carolina State University, Okinawa Institute of Science and Technology Graduate University, Ghent University, KU Leuven

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290