Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author's extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix-Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, (c) Birkhauser.
Richard P．Stanley，现任美国麻省理工学院数学系教授，是国际组合学界的领军人物之一。1971年获得美国哈佛大学博士学位，1988年当选美国艺术与科学院院土，1995年当选美国科学院院士。1975年获得工业与应用数学学会George Polya奖，2001年因两卷本《计数组合学》获得美国数学会Leroy P．Steele奖，2003年获得瑞典皇家科学院Rolf Schock奖，2006年受邀在国际数学家大会上作一小时学术报告。Stanley教授的研究成果清晰简明、深刻全面、极富创造力，促进了数学诸多方向的决定性进展。同时，他非常注重扶持和培养年轻学者，由他撰写的包括本书在内的教科书已成为国内外组合数学专业学生必读的经典范本。