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The Circuit-Cocircuit Intersection Conjecture for Intersection Size $k\le6$

Combinatorics 2021-12-24 v2

Abstract

Oxley conjectured (1992) that if a matroid has a circuit-cocircuit intersection of size k4k\ge4, it has a circuit-cocircuit intersection of size k2k-2. We show that this conjecture holds for k6k\le6.

Cite

@article{arxiv.2111.02605,
  title  = {The Circuit-Cocircuit Intersection Conjecture for Intersection Size $k\le6$},
  author = {Jaeho Shin},
  journal= {arXiv preprint arXiv:2111.02605},
  year   = {2021}
}

Comments

5 pages

R2 v1 2026-06-24T07:25:27.544Z