Vorträge in der Woche 14.04.2025 bis 20.04.2025

Mittwoch, 16.04.2025: Representation Classes of Arithmetic Matroids and their Cardinality

Tobias Schnieders (Tübingen)

When do given sets of vectors have the same combinatorial structure of linear independence relations between them? To answer this question, representation spaces of matroids are widely studied on vector spaces over fields. Arithmetic matroids were introduced in order to consider moduls over the integers instead of vector spaces. It turns out that every arithmetic matroid has at most finitely many representation classes up to a simple equivalence relation. I studied such representation classes and the possible numbers of representation classes an arithmetic matroid can or cannot have. Although they are not completely classified yet, some results and computations suggest a deep connection between these numbers and the image of Euler's totient function.