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}
}