Back to Search
Start Over
A separation between tropical matrix ranks
- Source :
- Proceedings of the American Mathematical Society. 151:489-499
- Publication Year :
- 2022
- Publisher :
- American Mathematical Society (AMS), 2022.
-
Abstract
- We continue to study the rank functions of tropical matrices. In this paper, we explain how to reduce the computation of ranks for matrices over the `supertropical semifield' to the standard tropical case. Using a counting approach, we prove the existence of a $01$-matrix with many ones and without large all-one submatrices, and we put our results together and construct an $n\times n$ matrix with tropical rank $o(n^{0.5+\varepsilon})$ and Kapranov rank $n-o(n)$.<br />Comment: 9 pages
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 151
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi.dedup.....a401c02b8db41a2d228d87759aa58b4b