Journal of Combinatorics
Volume 3 (2012)
Higher trivariate diagonal harmonics via generalized Tamari posets
Pages: 317 – 341
We consider the graded $S_n$-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 characteristics. This also leads to entirely new combinatorial formulas.
trivariate harmonics, r-Tamari poset
2010 Mathematics Subject Classification
Primary 05E10. Secondary 05A19.