1. Matroidal representations of low rank
- Author
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Jun, Jaiung, Mincheva, Kalina, and Tolliver, Jeffrey
- Subjects
Mathematics - Combinatorics ,Mathematics - Representation Theory ,12K10, 14T10, 05B35, 05E10 - Abstract
We study tropical subrepresentations of the Boolean regular representation $\mathbb{B}[G]$ of a finite group $G$. These are equivalent to the matroids on ground set $G$ for which left-multiplication by each element of $G$ is a matroid automorphism. We completely classify the tropical subrepresentations of $\mathbb{B}[G]$ for rank 3. When $G$ is an abelian group, our approach can be seen as a generalization of Golomb rulers. In doing so, we also introduce an interesting class of matroids obtained from equivalence relations on finite sets., Comment: The original submission (arXiv:2411.19883) was split into two parts, and this is the second. As a result, there is substantial overlap with the first
- Published
- 2025