4 citations · 10 across the 8 of their papers we have counts for
5 papers · 1 filter
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…
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…