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Lecture Notes in Computer Science 555 (1991), 108 123 ACKNOWLEDGMENTS 99 Acknowledgments MANY PEOPLE provided considerable help to the author as these notes were being prepared, notably Eli Goodman, Leo Guibas, Ricky Pollack, Jfirgen Richter-Gebert, David Satesin, Raimund Seidel, Bernd Sturmfels, Frances Yao, and Gfinter Ziegler. Special thanks are also due to Phyllis Winkler, who transformed more than 150 pages of scribbled manuscript into a respectable-looking scientific document. Some of the research was done during a visit to the Institute of Systems Science at the University of Singapore; the work was completed during a visit to Institut Mittag-Lemer in Djursholm, Sweden. @ 100 AXIOMS AND HULLS Bibliography [1] E. al-Aamily, A. O. Morris, and M. H. Peel, "The representations of the Weyl groups of type Bn," Journal of Algebra 68 (1981), 298-305. Cited on page 17. [2] Cecilia R. Aragon and Raimund G. Seidel, "Randomized search trees" (ex- tended abstract), 30th IEEE Symposium on Foundations of Computer Science (1989), 540-546. Cited on page 53. [3] Marshall Bern, David Eppstein, Paul Plassman, and Frances Yao, "Horizon theorems for lines and polygons," in Discrete and Computational Geometry: Papers from the DIMACS Special Year, edited by Jacob E. Goodman, Richard Pollack, and William Steiger, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 6 (1991), 45-66. Cited on page 96. [4] Marshall Bern, personal communication, January 1991. Cited on page 97. [5] Anders BjSrner, Michel Las Vergnas, Bernd Sturmfels, Neil White, and G/inter M. Ziegler, Oriented Matroids, Encyclopedia of Mathematics Series, Cam- bridge University Press (1992). Cited on page 97. [6] Robert G. Bland and Michel Las Vergnas, "Orientability of matroids," Journal of Combinatorial Theory B24 (1978), 94-123. Cited on pages 40, 95, 96, and 98. [7] J. Bokowski, G. Laffaille, and J. 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[17] Herbert Edelsbrunner and Ernst Peter M/icke, "Simulation of Simplicity: A technique to cope with degenerate cases in geometric algorithms," Fourth An- nual ACM Symposium on Computational Geometry (1988), 118-133. Cited on page 59. [18] H. Edelsbrunner, J. O'Rourke, and R. Seidel, "Constructing arrangements of lines and hyperplanes with applications," SIAM Journal on Computing 15 (1986), 341- 363. Cited on page 96. [19] H. Edelsbrunner, R. Seidel, and M. Sharir, "On the zone theorem for hyper- plane arrangements," SIAM Journal of Computing, to appear. Preprint in New Results and New Trends in Computer Science, edited by Hermann Man- rer, Lecture Notes in Computer Science 555 (1991), 108 123. Cited on page 96. [20] Robert W Floyd, personal communication, February 1964. Cited on page 29. [21] Jon Folkman and Jim Lawrence, "Oriented matroids," Journal of Combinato- rim Theory B25 (1978), 199-236. Cited on pages 40, 43, and 96. 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Knuth, "Two notes on notation," American Mathematical Monthly 99 (1992), 403-422. Cited on page 14. [47] Donald E. Knuth, The Stanford GraphBase, book in preparation. Cited on page 53. [48] Michel Las Vergnas, "Bases in oriented matroids," Journal of Combinatorial Theory B25 (1978), 283 289. Cited on pages 3, 40, and 95. [49] Michel Las Vergnas, "Convexity in oriented matroids," Jo,lrnal of Combinato- rial Theory B29 (1980), 231 243. Cited on page 96. [50] Alain Lascoux and Marcel-Panl Schiitzenberger, "Structure de Hopf de l'annean de cohomologie et de l'anneau de Grothendieck d'une vari6t~ de dra- peaux," Comptes Rendus des sdances de l'Acaddmie des Sciences, S~rie I, 295 (1982), 629 633. Cited on page 35. [51] Jim Lawrence, "Oriented matroids and multiply ordered sets," Linear Algebra and Its Applications 48 (1982), 1 12. Cited on pages 3 and 95. [52] F. 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