English

The maximum cardinality of minimal inversion complete sets in finite reflection groups

Representation Theory 2016-02-16 v3 Combinatorics

Abstract

We compute for reflection groups of type A,B,D,F4,H3A,B,D,F_4,H_3 and for dihedral groups a statistic counting the maximal cardinality of a set of elements in the group whose generalized inversions yield the full set of inversions and which are minimal with respect to this property. We also provide lower bounds for the EE types that we conjecture to be the exact value of our statistic.

Keywords

Cite

@article{arxiv.1312.7687,
  title  = {The maximum cardinality of minimal inversion complete sets in finite reflection groups},
  author = {Claudia Malvenuto and Pierluigi Möseneder Frajria and Luigi Orsina and Paolo Papi},
  journal= {arXiv preprint arXiv:1312.7687},
  year   = {2016}
}

Comments

Latex file, 23 pages. Major revision; title has changed. New results in types $F_4$ and $H_4$. To appear in Journal of Algebra