MATROID BASE POLYTOPES FOR SERIES-PARALLEL EXTENSIONS Kim, Sangwook;
In this article, we study the matroid base polytope for a matroid obtained from another matroid by a series or parallel extension of an element. We express this polytope as a wedge of a polytope. In particular, we provide the facial structure of the matroid base polytope corresponding to a series-parallel matroid.
matroid base polytopes;series-parallel matroids;
Andreas Brandstadt, Van Bang Le, and Jeremy P. Spinrad, Graph classes: a survey, SIAM Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999.
Eva Maria Feichtner and Bernd Sturmfels, Matroid polytopes, nested sets and Bergman fans, Port. Math. (N.S.), 62(4) (2005), 437-468.
I. M. Gel0fand, R. M. Goresky, R. D. MacPherson, and V. V. Serganova, Combinatorial geometries, convex polyhedra, and Schubert cells, Adv. in Math., 63(3) (1987), 301-316.
James G. Oxley, Matroid theory, Oxford Science Publications. The Clarendon Press Oxford University Press, New York, 1992.
David E. Speyer, Tropical linear spaces, SIAM J. Discrete Math., 22(4) (2008), 1527-1558.
Gunter M. Ziegler, Lectures on polytopes, volume 152 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995.