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math.CO2025
Metric graphs of negative type
Rutger Campbell, Kevin Hendrey, Ben Lund +1
The negative type inequalities of a metric space are closely tied to embeddability. A result by Gupta, Newman, and Rabinovich implies that if a metric graph does not contain a…
math.CO2024
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.CO2023
Average plane-size in complex-representable matroids
Rutger Campbell, Jim Geelen, Matthew E. Kroeker
Melchior's inequality implies that the average line-length in a simple, rank-, real-representable matroid is less than . A similar result holds for complex-representable matr…