Jonathan Boretsky

activity

20242026

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3 papers · 1 filter

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.CO2025

Polyhedral and Tropical Geometry of Flag Positroids

Jonathan Boretsky, Christopher Eur, Lauren Williams

A flag positroid of ranks $r := (r_{1} < \dots < r_{k})$ on $[n]$ is a flag matroid that can be realized by a real $r_{k} \times n$ matrix $A$ such that the $r_{i} \times r_{i}$ mino…

math.CO2024

On two notions of total positivity for generalized partial flag varieties of classical Lie types

Grant Barkley, Jonathan Boretsky, Christopher Eur +1

For Grassmannians, Lusztig's notion of total positivity coincides with positivity of the Plucker coordinates. This coincidence underpins the rich interaction between matroid theory…