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.
Hook length formulas for partially colored labeled forests / Fabrizio Caselli, Francesca Camagni. - In: JOURNAL OF COMBINATORICS. - ISSN 2156-3527. - STAMPA. - 8:4(2017), pp. 593-630.
Hook length formulas for partially colored labeled forests
Fabrizio Caselli;CAMAGNI, FRANCESCA
2017
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.