A statistic on the roots of a finite reflection group and a correspondence between the height function and Bruhat order

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156631The action of a finite reflection group (type A) on its set of roots is understood as a permutation representation or group action. We show that this representation is an induced representation from a certain kind of parabolic subgroup. Furthermore, we use this representation to define a statistic (derived from the length function) on the set of roots. A possible application to Costas Arrays is hinted at in a proposition.CombinatoricsGroup Theory20F55A statistic on the roots of a finite reflection group and a correspondence between the height function and Bruhat ordertext