Geodesic
The image of a tropical linear space
Joshua Mundinger1
1University of Wisconsin-Madison
The electronic journal of combinatorics, Tome 32 (2025) no. 1
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Given a tropical linear space $L \subseteq \mathbb{T}^n$ and a matrix $A \in \mathbb{T}^{m \times n}$, the image $AL$ of $L$ under $A$ is typically not a tropical linear space. We introduce a tropical linear space $\text{tropim}_{A}(L)$, the tropical image, containing $AL$. We show under mild hypotheses that $\text{tropim}_{A}(L)$ is realizable if $L$ is and apply the tropical image to construct the stable sum of two tropical linear spaces without a disjoint pair of bases.
DOI : 10.37236/13096
Classification : 14T15

Joshua Mundinger  1

1 University of Wisconsin-Madison 
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Joshua Mundinger. The image of a tropical linear space. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/13096

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