The Tropical Variety of Symmetric Rank 2 Matrices
Combinatorics
2025-04-21 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2404.08121,
title = {The Tropical Variety of Symmetric Rank 2 Matrices},
author = {May Cai and Kisun Lee and Josephine Yu},
journal= {arXiv preprint arXiv:2404.08121},
year = {2025}
}
Comments
21 pages, 8 figures, Version to appear in Linear Algebra and its Applications