Document Type
Lecture
Publication Date
11-20-2024
Abstract
Anelement of a matroid is free if it is contained in no circuits other than the spanning circuits. We call an element loose if it is contained in no circuits of size less than the rank of the matroid. Note that a matroid M is paving if and only if all elements of M are loose. In this talk, I will give a characterization of binary matroids that contain a loose element. For ternary matroids with a loose element, we show their size is linear in terms of their rank. Moreover, for a prime power q, we partially characterize all GF(q)-matroids that have two loose elements. Since all elements in a paving matroid are almost-loose, we note Rajpal’s partial characterization of GF(q)-paving matroids as a consequence. This is joint work with Tom Zaslavsky.
Relational Format
presentation
Recommended Citation
Singh, Jagdeep, "Loose elements and paving matroids" (2024). Combinatorics Seminar. 3.
https://egrove.olemiss.edu/math_combinatorics/3
