Journal of Combinatorics

Volume 8 (2017)

Number 4

Hook length formulas for partially colored labeled forests

Pages: 593 – 630



Francesca Camagni (Dipartimento di matematica, Università di Bologna, Italy)

Fabrizio Caselli (Dipartimento di matematica, Università di Bologna, Italy)


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

Received 31 August 2015

Published 17 July 2017