Zach Walsh

collaborators

4 papers

math.CO2026

Excluding a line from positroids

Jonathan Boretsky, Zach Walsh

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,…

math.CO2026

The unbreakable quasi-graphic matroids

Sayantani Bhattacharya, John David Clifton, Zach Walsh

A matroid M is unbreakable if it is connected and M/F is connected for every flat F of M . Oxley and Pfeil characterized the unbreakable graphic matroids, and Fife, Mayhew, Oxley,…

math.CO2026

Matroids from gain graphs over quotient groups

Zach Walsh

We present a new construction for matroids from gain graphs that simultaneously generalizes several existing constructions. The construction takes as input a gain graph over a Frob…

math.CO2025

TurÃ¡n densities for matroid basis hypergraphs

Jorn van der Pol, Zach Walsh, Michael C. Wigal

Let $U$ be a uniform matroid. For all positive integers $n$ and $r$ with $n \geq r$ , what is the maximum number of bases of an $n$ -element, rank- $r$ matroid without $U$ as a minor?…