Extensions and Deletions of Matroid Classes Closed Under Flats
MSU Affiliation
College of Arts and Sciences; Department of Mathematics and Statistics
Creation Date
2026-07-30
Abstract
We call a class of matroids hereditary if it is closed under restriction to flats. For a hereditary class M, its extension class consists of all matroids in M together with their single-element extensions. The deletion class consists of all matroids in M along with their single-element deletions. We prove that if 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.
Publication Date
6-2-2026
Publication Title
Advances in Applied Mathematics
Publisher
Elsevier
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Rights
© 2026 The Author(s)
Recommended Citation
Singh, J., & Sivaraman, V. (2026). Extensions and deletions of matroid classes closed under flats. Advances in Applied Mathematics, 180, 103118. https://doi.org/10.1016/j.aam.2026.103118
