Year: 2024
Type: article
Abstract: The type A cluster configuration space, commonly known as $\mathcal M_{0,n}$, is the very affine part of the binary geometry associated with the associahedron. The tropicalization of $\mathcal M_{0,n}$ can be realized as the space of phylogenetic trees and its signed tropicalizations as the dual-associahedron subfans. We give a concise overview of this construction and propose an extension to type C. The type C cluster configuration space $\mathcal M_{\mathrm C_l}$ arises from the binary geometry associated with the cyclohedron. We define a space of axially symmetric phylogenetic trees containing many dual-associahedron and dual-cyclohedron subfans. We conjecturally realize the tropicalization of $\mathcal M_{\mathrm C_l}$ as the defined space and its signed tropicalizations as the aforementioned subfans.
Source: Le Matematiche
Authors: Cox, Shelby, Makhlin, Igor
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4403580006