Algorithms, Combinatorics and Optimization Seminar
In Person - Wean Hall 8220
Ph.D. Student, Department of Mathematics, University of Washington
h-vector inequalities for weak maps of matroids
The study of matroids and their invariants has undergone remarkable developments in recent years. In particular, many long-standing conjectures concerning inequalities that are satisfied between certain invariants, such as the number of flats of a given rank, associated to a given matroid, have been resolved. We take a different perspective and consider inequalities between invariants of different matroids. By employing combinatorial and algebraic methods, we prove several results, with our main result being that the flag h-vector is nonincreasing under weak maps.