Séminaire Lotharingien de Combinatoire, 95B.60 (2026), 12 pp.
Jonathan Boretsky and Zach Walsh
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 U2,&ell+2 as a minor, and
characterize the positroids 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
U2,ℓ+2 as a minor. 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.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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