The image of a tropical linear space

2018/08/06 by Joshua Mundinger, Mundinger, Joshua
Computer Science · Mathematics · #14T #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1808.02150

openalex publication_date 2018/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a tropical linear space L ⊆ \mathbbTⁿ and a matrix A ∈ \mathbbT^{m × n}, the image AL of L under A is typically not a tropical linear space. We introduce a tropical linear space tropim_A(L), the tropical image, containing AL. We show under mild hypotheses that 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.

Citations

• Tropical Incidence Relations, Polytopes, and Concordant Matroids

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