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Algebraic Combinatorics and Coinvariant Spaces

Francois Bergeron

$221

Hardback

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English
A K Peters
06 July 2009
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.

By:  
Imprint:   A K Peters
Country of Publication:   United States
Dimensions:   Height: 229mm,  Width: 152mm, 
Weight:   498g
ISBN:   9781568813240
ISBN 10:   1568813244
Pages:   230
Publication Date:  
Audience:   College/higher education ,  Professional and scholarly ,  Further / Higher Education ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active

Bergeron, Francois

Reviews for Algebraic Combinatorics and Coinvariant Spaces

An abandoned kitten serves as balm, comic relief and social director to a hard-pressed Midwestern town.The feline came in through the book drop on a bone-crackingly cold winter's night. The place was the public library of Spencer, Iowa, where the corn grows nine feet high and the earth is so fertile you would swear the ground is about to push up and tip the sky right out of the picture. But this was in the 1980s, when the farm crisis was in full tilt; lenders had foreclosed on 50 percent of the family farms in northwest Iowa by the end of the decade. Local librarian Myron paints a town in crisis: economically, socially and in terms of the human spirit. She was in crisis too and neatly tucks her own recovery into the larger story of the town's gradual rejuvenation. Named Dewey (after the decimal system), the kitten became the library mascot and a synecdoche: He never lost his trust, no matter what the circumstances, or his appreciation for life He was confident. Myron doesn't overplay this metaphor, but works it subtly as she depicts the town's fortunes reviving and shows Dewey playing his role in that revival with composure, social skills, patience and a measure of mischief. In an easeful voice and with an eye for detail, she delineates Spencer: its economic swings, the lay of the land, the Prairie Deco downtown. Dewey is the pivot; he even became a bit of a national celebrity, and the New York Times ran his obit. He was, this loving account demonstrates, the right cat in the right place for Spencer and most certainly for its librarian.Intimate portrait of a place snugly set within its historical moment, preserved in Myron's understated, well-polished prose. (Kirkus Reviews)


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