arXiv Analytics

Sign in

arXiv:2310.18925 [math.CO]AbstractReferencesReviewsResources

Total positivity for matroid Schubert varieties

Xuhua He, Connor Simpson, Kaitao Xie

Published 2023-10-29Version 1

We define the totally nonnegative matroid Schubert variety $\mathcal Y_V$ of a linear subspace $V \subset \mathbb R^n$. We show that $\mathcal Y_V$ is a regular CW complex homeomorphic to a closed ball, with strata indexed by pairs of acyclic flats of the oriented matroid of $V$. This closely resembles the regularity theorem for totally nonnegative generalized flag varieties. As a corollary, we obtain a regular CW structure on the real matroid Schubert variety of $V$.

Related articles: Most relevant | Search more
arXiv:2401.15933 [math.CO] (Published 2024-01-29)
Acyclic matchings on Bruhat intervals and applications to total positivity
arXiv:1105.4170 [math.CO] (Published 2011-05-20)
KP solitons, total positivity, and cluster algebras
arXiv:1106.0023 [math.CO] (Published 2011-05-31, updated 2014-01-28)
KP solitons and total positivity for the Grassmannian