2 papers
math.CO2025
The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids
Matthew Baker, Oliver Lorscheid, Zach Walsh +1
We show that, under suitable hypotheses, the foundation of a generalized parallel connection of matroids is the relative tensor product of the foundations. Using this result, we sh…
math.CO2024
Foundations of matroids -- Part 2: Further theory, examples, and computational methods
Matthew Baker, Oliver Lorscheid, Tianyi Zhang
In this sequel to "Foundations of matroids - Part 1", we establish several presentations of the foundation of a matroid in terms of small building blocks. For example, we show that…