Speaker: William Schmitt, George Washington University
Title: The Free Product of Matroids
Abstract: We introduce a noncommutative binary operation on matroids, called the free product, and discuss some of its properties. In particular, free product is characterized by a certain universal property, is associative, and respects duality. We characterize the minors of the free product, and prove that, up to isomorphism, every matroid factors uniquely into matroids that are irreducible with respect to free product. We use these results to prove an inequality involving the numbers of nonisomorphic matroids on n elements which was conjectured by Welsh in 1969, and to prove the freeness of the algebra of matroids whose product is dual to the restriction-contraction coproduct .
Time: Friday, October 13, 2006, 3:30-4:20 p.m.Place: Science and Technology Building I, Room 242
Refreshments will be served before the talk at 3:00 p.m. in Room 222.
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491