Journal of Combinatorics

Volume 8 (2017)

Number 4

Hook length formulas for partially colored labeled forests

Pages: 593 – 630

DOI: http://dx.doi.org/10.4310/JOC.2017.v8.n4.a3

Authors

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

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

Abstract

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.

Keywords

complex reflection groups, flag-major index, invariant algebras

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Paper received on 31 August 2015.