PreprintarXiv licencearXiv
Dynamics of Transversal Matroids
Abstract
We propose a way of generating matroids by randomly picking indicator vectors, and since we will see that it mostly gives uniform matroids, which are transversal, we then look at randomly generated transversal matroids. In both models we also investigate threshold phenomena of certain monotone increasing properties. Non-monotone properties of transversal matroids will also be investigated. Moreover, we are going to see how to spot circuits of a transversal matroid from its bipartite graph presentation. In the last Chapter, we have a survey of the characterization of transversal matroids that admit acyclic bipartite presentations. We will also investigate when we can simplify a presentation for a transversal matroid.
Related
- On two problems concerning the geodesic transversal number of graphs
- Transversal Pooling Neural Networks
- Transversal Hölder Criteria and Dini--Zygmund Endpoint Regularity for Hyperbolic Harmonic Mappings
- Block Designs with Large Transversal-Block Intersections
- Deformations of Calabi--Yau varieties over transversal or crystalline prisms
BibTeX
@misc{lao2026dynamics,
title = {{Dynamics of Transversal Matroids}},
author = {Hin Lon Lao},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02586},
eprint = {2611.02586},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02586},
}
RIS
TY - UNPB
TI - Dynamics of Transversal Matroids
AU - Hin Lon Lao
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02586
UR - https://arxiv.org/abs/2611.02586
AB - We propose a way of generating matroids by randomly picking indicator vectors, and since we will see that it mostly gives uniform matroids, which are transversal, we then look at randomly generated transversal matroids. In both models we also investigate threshold phenomena of certain monotone increasing properties. Non-monotone properties of transversal matroids will also be investigated. Moreover, we are going to see how to spot circuits of a transversal matroid from its bipartite graph presentation. In the last Chapter, we have a survey of the characterization of transversal matroids that admit acyclic bipartite presentations. We will also investigate when we can simplify a presentation for a transversal matroid.
ER -