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The Q,T-Catalan Numbers and the Space of Diagonal Harmonics

Un libro in lingua di James Haglund edito da Amer Mathematical Society, 2008

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The field of algebraic combinatorics is dynamic, and one of the most lively studies within the field is the combinatorics of the space of diagonal harmonics. Haglund (mathematics, U. of Pennsylvania) works from his successful lectures here with discussions of topics in the theory of symmetric functions, including work at the practical level such as plethystic substitutions. He includes a substantial number of examples and exercises as he introduces q-analogues and symmetric functions and then moves to MacDonald polynomials and the space of diagonal harmonics, the q, t-Catalan numbers, the q, t-Schröder polynomial, parking functions and the Hilbert series, the shuffle conjecture, and the proof of the q, t-Schröder theorem. In appendices he provides information on the combinatorics of Macdonald polynomials and the Loehr-Warrington conjecture along with solutions to the exercises. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)

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