Applications of Sign Vectors and Elementary Vectors

Visit the repository on GitHub.

Conferences and Presentations

applications.dissertation_examples	Up-to-date examples of [Aic26].
applications.MoRN_2025	MoRN seminar software showcase 2025.
applications.ICMS_2024	Up-to-date examples of [AMR24].

Runtime Experiments

applications.runtime_circuits	Runtime of Circuits
applications.runtime_oriented_matroids	Runtime of Oriented Matroids
applications.runtime_certlin	Runtime of Certlin

Other Applications

applications.ecxs_symbolic

ECXs Symbolic Example of [MPSZ25].

References

[Aic26]

Marcus S. Aichmayr. “Computing Circuits and Sign Vectors with Applications to Linear Inequality Systems and Reaction Networks”. Submitted. PhD thesis. Kassel, Germany, 2026.

[AMR24]

Marcus S. Aichmayr, Stefan Müller, and Georg Regensburger. “A SageMath package for elementary and sign vectors with applications to chemical reaction networks”. In: Mathematical software—ICMS 2024 (2024), pp. 155–164. doi: 10.1007/978-3-031-64529-7_17.

[MHR19]

Stefan Müller, Josef Hofbauer, and Georg Regensburger. “On the bijectivity of families of exponential/generalized polynomial maps”. In: SIAM Journal on Applied Algebra and Geometry 3.3 (2019), pp. 412–438. doi: 10.1137/18M1178153.

[MPSZ25]

Stefan Müller, Michael Predl, Diana Széliová, and Jürgen Zanghellini. “Elementary vectors reveal minimal interactions in microbial communities”. In: bioRxiv (2025) doi: 10.1101/2025.07.30.667663.