Symmetric Kapranov and symmetric tropical ranks

2021/12/30 by Dylan Zwick, Zwick, Dylan
Computer Science · Mathematics · #05E14 (Secondary) #14T15 (Primary) 15A80 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2112.14945

openalex publication_date 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper proves the r × r minors of an n × n symmetric matrix of indeterminates are a tropical basis when r = 2, r = 3, or r = n, and are not when 4 < r < n or r = 4, n > 12. In the process, it introduces two new notions of rank for symmetric matrices coming from tropical geometry, the symmetric tropical and the symmetric Kapranov rank, which are the symmetric versions of their standard counterparts defined by Develin, Santos, and Sturmfels.

Related

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