Example of a 6-by-6 Matrix with Different Tropical and Kapranov Ranks

2010/12/26 by Yaroslav Shitov, Shitov, Yaroslav
Computer Science · Engineering · #15A03 #15A15 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1012.5507

openalex publication_date 2010/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an example of a 6-by-6 matrix with tropical rank equal to 4 and Kapranov rank equal to 5. This answers a question asked by M. Chan, A. Jensen, and E. Rubei.

Citations

• The 4x4 minors of a 5xn matrix are a tropical basis

Related

• On tropical and Kapranov ranks of tropical matrices
• On the rank of a tropical matrix
• A separation between tropical matrix ranks
• The 4x4 minors of a 5xn matrix are a tropical basis
• Symmetric Kapranov and symmetric tropical ranks