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

  • Emanuele Delucchi
  • Noriane Girard
  • Giovanni Paolini


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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