Work

The tropical variety of symmetric rank 2 matrices

Year: 2025

Type: article

Abstract: We study the tropicalization of the variety of symmetric rank two matrices. Analogously to the result of Markwig and Yu for general tropical rank two matrices, we show that it has a simplicial complex structure as the space of symmetric bicolored trees and that this simplicial complex is shellable. We also discuss some matroid structures arising from this space and present generating functions for the number of symmetric bicolored trees.

Source: Linear Algebra and its Applications

DOI: 10.1016/j.laa.2025.04.011

Authors: May Cai, Kisun Lee, Josephine Yu

Institutions: Georgia Institute of Technology, Clemson University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,230

Funders: National Science Foundation, Division of Mathematical Sciences