The Circuit-Cocircuit Intersection Conjecture for Intersection Size ≤7

2023/08/05 by Shin, Jaeho
#05B35 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.02859

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 k≥4 has a CCI of size k-2. We show that the conjecture holds for k≤7.

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