TAILIEUCHUNG - Báo cáo toán học: "Oriented Matroids Today"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Oriented Matroids Today. | Oriented Matroids Today Gunter M. Ziegler Department of Mathematics MA 7-1 Technische Universitat Berlin Strasse des 17. Juni 136 10623 Berlin Germany ziegler@ http . de ziegler Submitted October 6 1995 Accepted March 26 1996 Version 3 of September 10 1998. Mathematics Subject Classihcation 52-00 52B05 52B30 52B35 52B40 Abstract This dynamic survey offers an entry point for current research in oriented matroids. For this it provides updates on the 1993 monograph Oriented Matroids by Bjorner Las Vergnas Sturmfels White Ziegler 85 in three parts 1. a sketch of a few Frontiers of Research in oriented matroid theory 2. an update of corrections comments and progress as compared to 85 and 3. an extensive complete and up-to-date bibliography of oriented matroids comprising and extending the bibliography of 85 . 1 Introduction s . Oriented matroids are both important and interesting objects of study in Combinatorial Geometry and indispensable tools of increasing importance and applicability for many other parts of Mathematics. The main parts of the theory and some applications were in 1993 compiled in the quite comprehensive monograph by Bjorner Las Vergnas Sturmfels White Ziegler 85 . For other shorter introductions and surveys see Bachem Kern 35 Bokowski Sturmfels 146 Bokowski 116 Goodman Pollack 333 Ziegler 712 Chapters 6 and 7 and most recently Richter-Gebert Ziegler 565 . This dynamic survey provides three parts 1. a sketch of a few Frontiers of Research in oriented matroid theory 2. an update of corrections comments and progress as compared to 85 and 3. an extensive complete and up-to-date bibliography of oriented matroids comprising and extending the bibliography of 85 . Supported by a DFG Gerhard-Hess-Forschungsforderungspreis 1 THE ELECTRONIC JOURNAL OF COMBINATORICS 3 1996 DS 4 2 2 What is an Oriented Matroid Let V v1 v2 . vn be a finite spanning sequence of vectors in Rr that is a finite vector configuration. With this vector .

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