The Tropical Variety of Symmetric Rank 2 Matrices
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912333249380352 |
|---|---|
| author | Cai, May Lee, Kisun Yu, Josephine |
| author_facet | Cai, May Lee, Kisun Yu, Josephine |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Tropical Variety of Symmetric Rank 2 Matrices Cai, May Lee, Kisun Yu, Josephine Combinatorics Algebraic Geometry 14T15 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. |
| title | The Tropical Variety of Symmetric Rank 2 Matrices |
| topic | Combinatorics Algebraic Geometry 14T15 |
| url | https://arxiv.org/abs/2404.08121 |