Journal of Combinatorics

Volume 3 (2012)

Number 3

Higher trivariate diagonal harmonics via generalized Tamari posets

Pages: 317 – 341

DOI: http://dx.doi.org/10.4310/JOC.2012.v3.n3.a4

Authors

François Bergeron (Dept. Math., UQAM, Montréal, Canada)

Louis-François Préville-Ratelle (Dept. Math., UQAM, Montréal, Canada)

Abstract

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.

Keywords

trivariate harmonics, r-Tamari poset

2010 Mathematics Subject Classification

Primary 05E10. Secondary 05A19.

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