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

2017/06/20 by Delucchi, Emanuele, Girard, Noriane, Paolini, Giovanni · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.06360

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.

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