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}
}
  • Emanuele Delucchi, N. Girard, Giovanni Paolini
  • Published in Electr. J. Comb. 2017
  • Mathematics, Computer Science
  • 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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