English

Higher Trivariate Diagonal Harmonics via generalized Tamari Posets

Combinatorics 2015-03-19 v6 Representation Theory

Abstract

We consider the graded §n\S_n-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.

Keywords

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

R2 v1 2026-06-21T18:09:21.683Z