Mathematics and Statistics Seminar
Friday 4/8 Bear Hall 219
Thirty minutes before the talk coffee and cookies will be available in Bear Hall 211 at .
Speaker: Talmage James Reid
Department of Mathematics
University of Mississippi
Title: Clones in Representable Matroids
A matroid is a set system consisting of a finite set E together with a collection of subsets of E that are called independent. The independent sets satisfy axioms similar to those satisfied by linearly independent sets of vectors in a vector space. A matroid is representable over a field F if its set E can be taken as the columns of a matrix with entries in a field F. Subsets of columns will be independent if they are linearly independent as column vectors over F. A pair of elements x and y of a matroid are clones if the map that interchanges x and y and fixes all other elements is an isomorphism. We investigate clone sets in matroids that are representable over fields with few elements. This is joint work with Bonin, Cotwright, and Robbins.