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 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 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