arXiv subjects

Suho Oh

Publications and source records attributed to Suho Oh.

21 records · Page 2Linked to original sources

arXiv2010

Triangulations of $Δ_{n-1} \times Δ_{d-1}$ and Tropical Oriented Matroids

Develin and Sturmfels showed that regular triangulations of $Δ_{n-1} \times Δ_{d-1}$ can be thought as tropical polytopes. Tropical oriented matroids were defined by Ardila and Develin, and were conjectured to be in bijection with all subdivisions of $Δ_{n-1} \times Δ_{d-1}$. In this paper, we show that any triangulation of $Δ_{n-1} \times Δ_{d-1}$ encodes a tropical oriented matroid. We also suggest a new class of combinatorial objects that may describe all subdivisions of a bigger class of polytopes.

math.CO↗

arXiv2010

Positroids and Schubert matroids

Postnikov gave a combinatorial description of the cells in a totally-nonnegative Grassmannian. These cells correspond to a special class of matroids called positroid. We prove his conjecture that a positroid is exactly an intersection of permuted Schubert matroids. This leads to a nice combinatorial description of positroids that is easily computable.

math.CO↗

arXiv2007

Bruhat order, smooth Schubert varieties, and hyperplane arrangements

The aim of this article is to link Schubert varieties in the flag manifold with hyperplane arrangements. For a permutation, we construct a certain graphical hyperplane arrangement. We show that the generating function for regions of this arrangement coincides with the Poincare polynomial of the corresponding Schubert variety if and only if the Schubert variety is smooth. We give an explicit combinatorial formula for the Poincare polynomial. Our main technical tools are chordal graphs and perfect elimination orderings.

math.CO↗