English

The Circuit-Cocircuit Intersection Conjecture for Intersection Size $\le7$

Combinatorics 2023-08-08 v1

Abstract

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 k4k\ge4 has a CCI of size k2k-2. We show that the conjecture holds for k7k\le7.

Cite

@article{arxiv.2308.02859,
  title  = {The Circuit-Cocircuit Intersection Conjecture for Intersection Size $\le7$},
  author = {Jaeho Shin},
  journal= {arXiv preprint arXiv:2308.02859},
  year   = {2023}
}

Comments

5 pages, 1 figure

R2 v1 2026-06-28T11:48:51.079Z