Conjectures on Circuits and Clones in Matroids

by

Professor James Reid
University of Mississippi

ABSTRACT: Results on circuit sizes in matroids are given. For example, we give a generalization of Murty's characterization of the connected binary matroids with a unique circuit size. Results on clones in matroids are given. Two elements in a matroid are clones if the map that interchanges the elements and fixes all other elements is an automorphism. The uniform matroids are the matroids with a unique clone set. We consider matroids with few clone sets.