The q,t-Catalan numbers naturally occur in the study of Macdonald polynomials and Hilbert schemes. Haiman and Garsia-Haglund independently proved that they are polynomials of q and t with nonnegative coefficients. We give simple upper bounds on coefficients in terms of partition numbers, and find all coefficients which achieve the bounds. The main idea is to develop a nontrivial morphism from the space of alternating polynomials to partitions. This is a joint work with Li Li.