Showing math.COShow all
3 papers · 1 filter
math.CO2025
Rainbow triangles and the ErdÅs-Hajnal problem in projective geometries
Carolyn Chun, James Dylan Douthitt, Wayne Ge +3
We formulate a geometric version of the ErdÅs-Hajnal conjecture that applies to finite projective geometries rather than graphs, in both its usual 'induced' form and the multicolo…
math.CO2025
Characterizing real-representable matroids with large average hyperplane-size
Rutger Campbell, Matthew E. Kroeker, Ben Lund
Generalizing a theorem of the first two authors and Geelen for planes, we show that, for a real-representable matroid , either the average hyperplane-size in is at most a co…
math.CO2024
A Sylvester-Gallai-type theorem for complex-representable matroids
Jim Geelen, Matthew E. Kroeker
The Sylvester-Gallai Theorem states that every rank- real-representable matroid has a two-point line. We prove that, for each , every complex-representable matroid with…