Higher Trivariate Diagonal Harmonics via generalized Tamari Posets
Combinatorics
2015-03-19 v6 Representation Theory
Abstract
We consider the graded -modules of higher diagonally harmonic polynomials in three sets of variables (the trivariate case), and show that they have interesting ties with generalizations of the Tamari poset and parking functions. In particular we get several nice formulas for the associated Hilbert series and graded Frobenius characteristic. This also leads to entirely new combinatorial formulas.
Cite
@article{arxiv.1105.3738,
title = {Higher Trivariate Diagonal Harmonics via generalized Tamari Posets},
author = {F. Bergeron and L. -F. Preville-Ratelle},
journal= {arXiv preprint arXiv:1105.3738},
year = {2015}
}
Comments
14 pages, 1 figure. Clarification of some sections, and typos correction