Algebraic and enumerative combinatorics seminar - Jonathan Boretsky-Excluding a line from positroids

Abstract: For all positive integers l and r, we determine the maximum number of elements of a simple rank-r positroid without the rank-2 uniform matroid U(2, l+2) as a minor, and characterize the matroids with the maximum number of elements. This result continues a long line of research into upper bounds on the number of elements of matroids from various classes that forbid U(2, l+2) as a minor, including works of Kung, of Geelen–Nelson, and of Geelen–Nelson–Walsh. This is the first paper to study positroids in this context, and it suggests methods to study similar problems for other classes of matroids, such as gammoids or base-orderable matroids. This project is based on joint work with Zach Walsh.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.