4 citations · 10 across the 8 of their papers we have counts for
8 papers
The Circuit-Cocircuit Intersection Conjecture for Intersection Size
Jaeho Shin
A circuit-cocircuit intersection, or a CCI for short, of a matroid is the intersection of a circuit and a cocircuit. Oxley conjectured (1992) that a matroid with a CCI of size $k\g…
The Circuit-Cocircuit Intersection Conjecture for Intersection Size
Jaeho Shin
Oxley conjectured (1992) that if a matroid has a circuit-cocircuit intersection of size , it has a circuit-cocircuit intersection of size . We show that this conjecture…
The Sticky Matroid Conjecture
Jaeho Shin
We show Kantor's conjecture (1974) holds in rank 4. This proves both the sticky matroid conjecture of Poljak and Turzik (1982) and the whole Kantor's conjecture, due to an argument…
Realizable Sticky Matroid Conjecture
Jaeho Shin
We give a criterion for modular extension of rank-4 hypermodular matroids, and prove a weakening of Kantor's conjecture for rank-4 realizable matroids. This proves the sticky matro…
Biconvex Polytopes and Tropical Linear Spaces
Jaeho Shin
A biconvex polytope is a classical and tropical convex hull of finitely many points. Given a biconvex polytope, for each vertex of it we construct a directed bigraph and a gammoid…
Birational Geometry of Matroids and Abstract Hyperplane Arrangements
Jaeho Shin
A matroid is a machine capturing linearity of mathematical objects and producing combinatorial structures. Matroid structure arises everywhere since linearity is a ubiquitous conce…
Extended Torelli map to the Igusa blowup in genus 6, 7, and 8
Valery Alexeev, Ryan Livingston, Joseph Tenini +7
It was conjectured in \cite{Namikawa_ExtendedTorelli} that the Torelli map associating to a curve its jacobian extends to a regular map from the Deligne-Mumford moduli…
Cohomology of quantum groups: An analog of Kostant's Theorem
University of Georgia VIGRE Algebra Group, Irfan Bagci, Brian D. Boe +8
We prove the analog of Kostant's Theorem on Lie algebra cohomology in the context of quantum groups. We prove that Kostant's cohomology formula holds for quantum groups at a generi…