Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
Title: Cyclic flat approach to matroid base polytopes
Speaker: | Ahmed Ashraf |
Affiliation: | Western University |
Room: | MC 5501 |
Abstract: Ardila, Benedetti and Doker realised matroid polytopes as generalized permutohedra, and using the work of Postnikov, gave an expression of volume of a matroid polytope, in terms of a sum of products of Crapo's beta invariants of certain matroid minors. On the other hand, Derksen and Fink in their joint paper have proved universality of a valuative invariant for matroids, defined previously by Derksen. Recently, motivated by tropical geometry, Hampe defined the notion of matroid intersection ring and showed that it is generated additively by loopless Schubert matroids. Using these ideas, we describe another approach to finding volume of a base polytope from lattice of cyclic flats of its respective matroid. As an application, we give a closed formula for the volumes of connected (sparse) paving matroid polytopes.
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.