The number of lines in a matroid with no U_2,n-minor

2013/06/11 by Jim Geelen, Peter Nelson, Geelen, Jim +1
Computer Science · Engineering · Mathematics · Neuroscience · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Nuclear Receptors and Signaling #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1306.2387

arxiv created 2013/06/11 · openalex publication_date 2013/06/11 · arxiv updated 2013/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, if q is a prime power at most 5, then every rank-r matroid with no U_2,q+2-minor has no more lines than a rank-r projective geometry over GF(q). We also give examples showing that for every other prime power this bound does not hold.

Related

• Matroids with no U_2,n-minor and many hyperplanes
• The number of rank-k flats in a matroid with no U_2,n-minor
• The smallest matroids with no large independent flat
• Excluding a line from positroids
• Projective geometries in exponentially dense matroids. I