Higher trivariate diagonal harmonics via generalized Tamari posets

• DOI: 10.4310/joc.2012.v3.n3.a4
• Publication Date: 2013-08-30T19:24:42Z
• Authors: François Bergeron; Louis-François Pr...
• Keywords: 0101 mathematics; 01 natural sciences

We consider the graded S n -modules of higher diagonally harmonic polynomials in three sets variables (the trivariate case), and show that they have interesting ties with generalizations Tamari poset parking functions.In particular we get several nice formulas for associated Hilbert series Frobenius characteristics.This also leads to entirely new combinatorial formulas.