Year: 2025
Type: article
Abstract: We point out to a connection of an old approach of Gondran and Minoux to ranks of matrices over the algebra ( ℝ , max , + ) and a recent work of Brandenburg, Loho, and Sinn on positive tropicalizations of algebraic varieties. This leads to examples of tropical varieties and their tropical bases which are not the corresponding positive tropical generating sets. In particular, we show that the d × d minors of a d × n matrix of variables form a positive tropical generating set if and only if either (1) d = n or (2) d ⩽ 4 .
Source: Algebraic Combinatorics
DOI: 10.5802/alco.440
Author: Yaroslav Shitov
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415736007