Extensions and deletions of matroid classes closed under flats
Abstract
We call a class of matroids hereditary if it is closed under restriction to flats. For a hereditary class $\mathcal{M}$, its extension class consists of all matroids in $\mathcal{M}$ together with their single-element extensions. The deletion class consists of all matroids in $\mathcal{M}$ along with their single-element deletions. We prove that if $\mathcal{M}$ has finitely many forbidden flats, then the forbidden flats for its extension class have bounded rank. For $GF(q)$-representable matroids where $q$ is in $\{2,3\}$, we exploit correspondence with $2$-colorings of projective geometries to establish the analogous result for the deletion class. We also note the consequences for hereditary classes of graphs, discussing the interplay of graphs and matroids.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Machine Learning and Algorithms
Publication details
- Journal / source
- Advances in Applied Mathematics
- Publisher
- Elsevier BV
- Volume
- 180
- Pages
- 103118–103118
- Publication date
- 2 June 2026
- Language
- EN