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Stanley-Reisner rings for quasi-arithmetic matroids

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arxiv 1709.03834 v1 pith:GCS4HLNY submitted 2017-09-12 math.CO math.AC

Matthias Lenz This is my paper · ORCID
classification math.COmath.AC
keywords matroidsquasi-arithmeticstanley-reisnercomplexesdefineringsassociatedconstruction
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In this note we define a Stanley-Reisner ring for quasi-arithmetic matroids and more general structures. To this end, we define two types of CW complexes associated with a quasi-arithmetic matroid that generalize independence complexes of matroids. Then we use Stanley's construction of Stanley-Reisner rings for simplicial posets.

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  1. Representations of torsion-free arithmetic matroids

    math.CO 2019-08 conditional novelty 7.0 of 10

    A new reduction and signed Hermite normal form let every representation of a torsion-free arithmetic matroid be computed up to equivalence, yielding a sharpened upper bound and counterexamples to two shellability conjectures.

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