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Author Orlik, Peter, 1938-

Title Algebraic combinatorics : lectures at a summer school, Nordfjordeid, Norway, June, 2003 / Peter Orlik, Volkmar Welker
Published Berlin ; London : Springer, 2007
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Description 1 online resource (viii, 177 pages) : illustrations
Series Universitext
Universitext.
Contents PART I. LECTURES ON ARRANGEMENTS. Introduction -- 1. Algebraic combinatorics. Chamber counting. Ranking patterns. Random walks. The Orlik-Solomon algebra. The NBC complex. The Aomoto complex. Combinatorial types. Formal connections. Multiplicities. Ideal invariance. Examples. Exercises. -- 2. Applications. Topology. Local system cohomology. Resonance. Moduli spaces. Gauss-Manin connections. Exercises. -- References -- PART II. DISCRETE MORSE THEORY AND FREE RESOLUTIONS. 1. Introduction. Overview. Enumerative and algebraic invariants of simplicial complexes. Cohen-Macaulay simplicial complexes. Some open problems in the field -- 2. Basic definitions and examples. Multigraded free resolutions. Basics of CS-complexes. Basics of cellular homology. Cellular chain complexes and cellular resolutions. Co-Artinian monomial modules -- 3. Cellular resolution. When does a CS-complex support a cellular resolution? Reading off the Betti numbers. Examples of cellular resolutions -- 4. Discrete Morse theory. Forman's discrete Morse theory. Discrete Morse theory for graded CW-complexes. Minimizing cellular resolutions using discrete Morse theory. The Morse differential -- References -- Index
Bibliography Includes bibliographical references (pages 169-172) and index
Notes English
Print version record
Subject Combinatorial geometry.
Free resolutions (Algebra)
Form Electronic book
Author Welker, Volkmar.
ISBN 3540683755 (paperback)
3540683763
9783540683759 (paperback)
9783540683766