English

Shellability of posets of labeled partitions and arrangements defined by root systems

Combinatorics 2017-06-21 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1706.06360,
  title  = {Shellability of posets of labeled partitions and arrangements defined by root systems},
  author = {Emanuele Delucchi and Noriane Girard and Giovanni Paolini},
  journal= {arXiv preprint arXiv:1706.06360},
  year   = {2017}
}