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Algebraic Combinatorics and Coinvariant Spaces (Cms Treatises in Mathematics/ Traites De Mathematiques De La Smc)

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Algebraic Combinatorics and Coinvariant Spaces (Cms Treatises in Mathematics/ Traites De Mathematiques De La Smc) image
ISBN-10:

1568813244

ISBN-13:

9781568813240

Author(s): Bergeron, François
Edition: 1
Released: Jul 06, 2009
Publisher: AK Peters/CRC
Format: Hardcover, 230 pages
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Description:

Written for graduate students in mathematics or non-specialist mathematicians who wish to learn the basics about some of the most important current research in the field, this book provides an intensive, yet accessible, introduction to the subject of algebraic combinatorics. After recalling basic notions of combinatorics, representation theory, and some commutative algebra, the main material provides links between the study of coinvariant―or diagonally coinvariant―spaces and the study of Macdonald polynomials and related operators. This gives rise to a large number of combinatorial questions relating to objects counted by familiar numbers such as the factorials, Catalan numbers, and the number of Cayley trees or parking functions. The author offers ideas for extending the theory to other families of finite Coxeter groups, besides permutation groups.

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