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Shellability of posets of labeled partitions and arrangements defined by root systems
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We prove that the posets of connected components of intersections of toric and elliptic arrangements defined by root systems are EL-shellable and we compute their homotopy type. Our method rests on Bibby's description of such posets by means of "labeled partitions": after giving an EL-labeling and counting homology chains for general posets of labeled partitions, we obtain the stated results by considering the appropriate subposets.
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Representations of torsion-free arithmetic matroids
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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