Journal of Combinatorics
Volume 8 (2017)
Hook length formulas for partially colored labeled forests
Pages: 593 – 630
Motivated by the study of the invariant theory of some finite groups, we introduce and study the notion of partially colored labeled forest. A flag-major index is defined on these forests and we study the distribution of this statistic on all partially colored labeled forests and on linear extensions of a fixed partially colored labeled forest. The main results that we obtain are formulas for such distributions which have a very simple factorization form and generalize and unify several known results present in the literature.
complex reflection groups, flag-major index, invariant algebras
Paper received on 31 August 2015.