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Square $\boldsymbol {q,t}$-lattice paths and $\boldsymbol {\nabla (p_n)}$

2006
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Transactions of the American Mathematical Society
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The combinatorial q, t-Catalan numbers are weighted sums of Dyck paths introduced by J. Haglund and studied extensively by Haglund, Haiman, Garsia, Loehr, and others. The q, t-Catalan numbers, besides having many subtle combinatorial properties, are intimately connected to symmetric functions, algebraic geometry, and Macdonald polynomials. In particular, the n'th q, t-Catalan number is the Hilbert series for the module of diagonal harmonic alternants in 2n variables; it is also the coefficient

doi:10.1090/s0002-9947-06-04044-x
fatcat:rhrmjcvtmzaenob6p5nblddioi