By James Haglund
This booklet includes designated descriptions of the numerous fascinating fresh advancements within the combinatorics of the gap of diagonal harmonics, a subject matter on the vanguard of present study in algebraic combinatorics. those advancements led in flip to a few amazing 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 quarter which includes symmetric services or lattice direction combinatorics. The publication includes expository discussions of a few subject matters within the conception of symmetric services, reminiscent of the sensible makes use of of plethystic substitutions, which aren't handled extensive in different texts. workouts are interspersed through the textual content in strategic destinations, with complete suggestions given in Appendix C.
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