Download E-books The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics (University Lecture Series) PDF

By James Haglund

This ebook includes exact descriptions of the numerous fascinating fresh advancements within the combinatorics of the gap of diagonal harmonics, a subject on the leading edge of present study in algebraic combinatorics. those advancements led in flip to a few incredible discoveries within the combinatorics of Macdonald polynomials, that are defined in Appendix A. The publication is acceptable as a textual content for a themes path in algebraic combinatorics, a quantity for self-study, or a reference textual content for researchers in any region which includes symmetric capabilities or lattice course combinatorics. The publication includes expository discussions of a few subject matters within the idea of symmetric capabilities, comparable to the sensible makes use of of plethystic substitutions, which aren't taken care of intensive in different texts. routines are interspersed during the textual content in strategic destinations, with complete options given in Appendix C.

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