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arxiv: 2404.08121 · v2 · pith:PAWELE4G · submitted 2024-04-11 · math.CO · math.AG

The Tropical Variety of Symmetric Rank 2 Matrices

May Cai , Kisun Lee , Josephine Yu This is my paper

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classification math.CO math.AG
keywords symmetricmatricesrankbicoloredcomplexsimplicialspacetrees
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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.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Copositive Matrices with Ordered Off-Diagonal Entries

    math.OC 2026-05 unverdicted novelty 7.0

    Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.