New Perspectives in Algebraic Combinatorics
New Perspectives in Algebraic Combinatorics by Louis J. Billera, published by Cambridge University Press on September 28, 1999, is a comprehensive exploration of combinatorial problems linked to various branches of mathematics. This edition spans 345 pages and is presented in English, offering insights from a full academic-year program held at MSRI during 1996-97, which focused on the intersections of combinatorics with algebraic geometry, topology, and other mathematical fields.
Readers will find a collection of expository articles that delve into topics such as matroid bundles, combinatorial representation theory, and the enumeration of matchings. The contributions, authored by respected researchers, aim to present the current state of the art in combinatorics, making this book a valuable resource for graduate students and researchers interested in the connections between combinatorics, algebra, and geometry. The text serves as a detailed account of the seminars conducted during the program, highlighting significant advancements and ongoing discussions in the field.
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During 1996-97 MSRI held a full academic-year program on combinatorics, with special emphasis on its connections to other branches of mathematics, such as algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. The rich combinatorial problems arising from the study of various algebraic structures are the subject of this book, which features work done or presented at the program’s seminars. The text contains contributions on matroid bundles, combinatorial representation theory, lattice points in polyhedra, bilinear forms, combinatorial differential topology and geometry, Macdonald polynomials and geometry, enumeration of matchings, the generalized Baues problem, and Littlewood-Richardson semigroups. These expository articles, written by some of the most respected researchers in the field, present the state of the art to graduate students and researchers in combinatorics as well as in algebra, geometry, and topology.
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