3 papers
math.CO2026
Comparability in Bruhat orders
Jonathan Boretsky, Alvaro Cornejo, Reuven Hodges +3
We determine the sharp asymptotic scale of the probability that two uniformly random permutations are comparable in weak Bruhat order, showing that $\mathbb{P}(σ_1 \preceq_W σ_2)=\…
math.CO2024
Totally positive skew-symmetric matrices
Jonathan Boretsky, Veronica Calvo Cortes, Yassine El Maazouz
A matrix is totally positive if all of its minors are positive. This notion of positivity coincides with the type A version of Lusztig's more general total positivity in reductive…
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…