Stefan Kaspar | Searcharxiv

arXiv2026

On the Possibilities of Defining Infinite Oriented Matroids

Is it possible to define cryptomorphic axiom systems for infinite oriented matroids by lifting some of the axiom systems for finite oriented matroids to the infinite setting while not losing duality in the process? We show that the answer to this question is a twofold "no". First, lifting the circuit axioms neither preserves duality nor inheritance of strong circuit elimination in minors. Second, although duality is kept intact by translating the orthogonality axioms and an axiom system based on the Farkas Lemma, the classes of infinite oriented matroids obtained in this way have the property that one is a proper subclass of the other.

math.CO↗

arXiv2011

Computing Border Bases without using a Term Ordering

Border bases, a generalization of Groebner bases, have actively been researched during recent years due to their applicability to industrial problems. A. Kehrein and M. Kreuzer formulated the so called Border Basis Algorithm, an algorithm which allows the computation of border bases that relate to a degree compatible term ordering. In this paper we extend the original Border Basis Algorithm in such a way that also border bases that do not relate to any term ordering can be computed by it.

math.AC↗