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Combinatorics of Tesler matrices in the theory of parking functions and diagonal harmonics. (English) Zbl 1291.05203
Summary: In [J. Haglund, Adv. Math. 227, No. 5, 2092–2106 (2011; Zbl 1258.13020)], the study of the Hilbert series of diagonal coinvariants is linked to combinatorial objects called Tesler matrices. In this paper we use operator identities from Macdonald polynomial theory to give new and short proofs of some of these results. We also develop the combinatorial theory of Tesler matrices and parking functions, extending results of P. Levande, and apply our results to prove various special cases of a positivity conjecture of Haglund [loc. cit.].

MSC:
05E05 Symmetric functions and generalizations
33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
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