Document Type
Lecture
Publication Date
10-12-2009
Abstract
A matroid is a pair (E,I) where E is a finite set and I is a collection of subsets of E that satisfies the following axioms: 1) I; 2) if I I and I I, then I mathcalI; 3) if I,J I and|I| < |J|, thenthereexists x J\I suchthatI {x} I. Two elements x and y of a matroid M are clones if the map that interchanges x and y and that fixes all other elements is an automorphism of M. It is clear that if E is the set of columns of a matrix over a field and I is the collection of subsets of E that are linearly independent, then (E,I) is a matroid. Such a matroid is essentially a sub-structure of the projective space over that field. We study clones in matroids that arise from matrices over a finite field. This is joint work with Reid, Robbins, and Wu.
Relational Format
presentation
Recommended Citation
Zhou, Xiangqian, "Clones in representable matroids over a finite field" (2009). Combinatorics Seminar. 78.
https://egrove.olemiss.edu/math_combinatorics/78
