William R. Schmitt

Ph.D., Massachusetts Institute of Technology, 1986


    Department of Mathematics
   Monroe Hall, Room 266
   The George Washington University
   2115 G Street, NW
   Washington, DC, 20052

       Phone:   (202) 994-3138
Fax:   (202) 994-6760
Email:   wschmitt@gwu.edu

Photos:   Me    Mini Me


Research Interests

Combinatorics and algebra, with specific interest in enumeration theory, partially ordered sets, matroid theory, Hopf algebras and category theory.

Selected Papers

  1. Primitive elements in the matroid-minor Hopf algebra, preprint, 20 pages (coauthor: H. Crapo).
  2. Renormalization as a functor on bialgebras, Journal of Pure and Applied Algebra, to appear, 22 pages (coauthor: C. Brouder).
  3. A unique factorization theorem for matroids, Journal of Combinatorial Theory A 112 (2005), 222-249 (coauthor: H. Crapo). 
  4. The free product of matroids, European Journal of Combinatorics 26 (2005), 1060-1065 (coauthor: H. Crapo). 
  5. A free subalgebra of the algebra of matroids, European Journal of Combinatorics, 26 (2005), 1066-1085 (coauthor: H. Crapo). 
  6. The Whitney algebra of a matroid, Journal of Combinatorial Theory A 91 (2000), 215-263.  
  7. Hopf algebra methods in graph theory, Journal of Pure and Applied Algebra 101 (1995), 77-90.  
  8. Incidence Hopf algebras, Journal of Pure and Applied Algebra 96 (1994), 299-330.  
  9. Hopf algebras of combinatorial structures, Canadian Journal of Mathematics 45 (1993), 412-428.  
  10. Coclosure operators and chromatic polynomials, Proceedings of the National Academy of Sciences 87 (1990), 4685-4687 (coauthor: N. Ray). 

Expository Writing

  1. A concrete introduction to category theory (60 pages, pdf). An introduction to category theory, with emphasis on examples from combinatorics and elementary algebra.
  2. Notes on modules and algebras (15 pages, pdf).  Notes written to provide students with necessary background for a course on Hopf algebras in combinatorics.


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Updated 5 September 2007.