Έλλεν Εμίλια Άννα Zscheile's public documents

I'm B. Sc. Έλλεν Εμίλια Άννα Zscheile and I currently study mathematics at RWTH Aachen University, after switching to here from the University of Technology Chemnitz.

Blog

2024, August: Started researching Neil White's conjecture after stumbling across it on the Wikipedia page "Basis of a matroid", while preparing for an exam on discrete mathematics.
2024, November: "On relation-transformations for relations with equal margin sizes", a talk at the Research Seminar of algorithmic and discrete mathematics, at the University of Technology Chemnitz
2025, April: My Bachelor thesis: Neil White’s Conjecture: Combinatorial and Algebraic Approaches done at Chemnitz University of Technology

A highlight of this is that instances of Neil White's conjecture can be represented via bipartite graphs on points and positions.
2025, August: Graphs and transitive closures describes how disconnecting a generated graph (on matroid basis tuples) by modifications of the original one also disconnects the original one.
2026, April: Resolving matroid circuit exchanges discusses a way to decompose matroid circuit exchanges.
2026, April/May: Circuit exchanges and the toric ideal of a matroid boils the previous working paper down to its essence and manages to prove that the toric ideal of a matroid is generated in degree at most 3, as long as the ideal of generators of symmetric exchanges and triangle cyclic exchanges fulfill a factoring constraint.
2026, May/June: Justifying division in basis systems proves just that missing factoring constraint.

2025: planar-incr-embed concepts deep dive, an in-depth introduction to the concepts behind the planar-incr-embed backend and incremental computation of planar embeddings.
2026 [work in progress]: An introduction of planar complexes, an attempt to formalize the concepts behind planar-incr-embed (not particularly successful so far).
2026, July/August: The diagonal taxicab norm [HTML version]