Tuesday, Nov 9, 3pm EST (8pm GMT, 9am Wed NZDT)
Dillon Mayhew, Victoria University of Wellington
Matroids that are transversal and cotransversal
Transversal matroids can be understood geometrically as those matroids obtained by placing points as freely as possible on the faces of a simplex. Transversal matroids have been studied extensively since their discovery in 1965. This study is made more challenging by the fact that the class of transversal matroids is not closed under duality or under taking minors.
Less work has been done on the matroids that are both transversal and cotransversal (a matroid is cotransversal if its dual is transversal). My belief is that the class of such matroids should behave a little like matroids representable over a finite field. I will talk about this class with reference to decidable theories, well-quasi-ordering, and the complexity of testing membership. I would also like to know more about minor-closed classes of matroids that are transversal and cotransversal. I have many more questions than answers.