Year: 2026
Type: preprint
Abstract: We give an example showing that the dual of an algebraic matroid need not be algebraic. Our example is a matroid of rank 6 on 10 elements which is algebraic in characteristic 2. It is obtained by gluing an algebraic realization of the non-Fano matroid to a realization of the Fano matroid. Its dual is shown not to be algebraic using the Ingleton-Main lemma.
Source: arXiv (Cornell University)
Authors: Larson, Matt, Le, Tuong
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7207781552