# Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems

@article{Delucchi2017ShellabilityOP, title={Shellability of Posets of Labeled Partitions and Arrangements Defined by Root Systems}, author={Emanuele Delucchi and N. Girard and Giovanni Paolini}, journal={Electr. J. Comb.}, year={2017}, volume={26}, pages={P4.14} }

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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