On the Folkman-Lawrence Topological Representation Theorem for Oriented Matroids of Rank 3

European Journal of Combinatorics

Volumn 22, Issue 5, 2001, Pages 601-615

  Bokowski, Jürgen ^a   Mock, Susanne ^a   Streinu, Ileana ^b  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b SMITH COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035645211     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1006/eujc.2000.0482     Document Type: Article

References (24)

1. A. Altshuler, J. Bokowski and S. Steinberg, The classification of simplicial 3-spheres with nine vertices into polytopes and non-polytopes, Discrete Math., 31 (1980), 115-124.
2. C. Antonin, Ein Algorithmusansatz für Realisierungsfragen im E getestet an kombinatorischen 3-Sphären, Staatsexamensarbeit, Bochum, 1982.
3. A. Björner, M. Las Vergnas, B. Sturmfels, N. White and G. Ziegler, Oriented Matroids, Cambridge University Press, Cambridge, U.K., 1993.
4. J. Bokowski, Oriented Matroids, in [13], 1993, pp. 555-602.
5. J. Bokowski and A. Guedes de Oliveira, On the generation of oriented matroids, Discrete Comput. Geom., 24 (2000), 197-208.
6. R. Cordovil, Sur les matroïdes orientés de rang 3 et les arrangements de pseudodroites dans le plan projectif réel, Europ. J. Combinatorics, 3 307-318.
7. J. Edmonds and A. Mandel, Topology of Oriented Matroids, Abstract 758-05-9, Notices of the American Mathematical Society, 25, 1978, p. A-410; also Ph.D. Thesis of A. Mandel, University of Waterloo, 1982.
8. J. Edmonds and A. Mandel, Topology of Oriented Matroids, Abstract 758-05-9, Notices of the American Mathematical Society, 25, 1978, p. A-410; also Ph.D. Thesis of A. Mandel, University of Waterloo, 1982.
9. S. Felsner and H. Weil, Sweeps, arrangements and signotopes, preprint, 1998.
10. J. Folkman and J. Lawrence, Oriented matroids, J. Comb. Theory, Ser. B, 25 (1978), 199-236.
11. J. E. Goodman, Pseudoline Arrangements, in [11], 1997, pp. 83-110.
12. J. E. Goodman and J. O'Rourke (eds), Handbook of Combinatorial and Computational Geometry, CRC Press, Boca Raton, FL, 1997.
13. J. E. Goodman and R. Pollack, Semispaces of configurations, cell complexes of arrangements, J. Comb. Theory, Ser. A, 37 (1984), 257-293.
14. P. M. Gruber and J. M. Wills (eds), Handbook of Convex Geometry, Vol. A and B, North-Holland, Amsterdam, 1993.
15. B. Grünbaum, Arrangements and Spreads, Regional Conf. Ser. Math., American Mathematical Society, 10, Providence, RI, 1972.
16. W. Hochstättler, Seitenflächenverbande orientierter matroide, Ph.D. Thesis, Köln, 1992.
17. D. E. Knuth, Axioms and Hulls, Springer Verlag, New York, 1992.
18. M. Las Vergnas, Matroïdes orientables, C.R. Acad. Sci., Paris, Ser. A, 280 (1975), 61-64.
19. M. Las Vergnas, Bases in oriented matroids, J. Comb. Theory, Ser. B, 25 (1978), 283-289.
20. J. Lawrence, Oriented matroids and multiply ordered sets, Linear Algebr. Appl., 48 (1982), 1-12.
21. F. Levi, Die Teilung der projektiven Ebene durch Gerade oder Pseudogerade, Ber. Verh. Sächs. Ges. Wiss. Leipzig, Math. Phys. Kl., 78 (1926), 256-267.
22. J. O'Rourke and I. Streinu, Pseudo-visibility graphs: characterization and recognition, Proc. Symp. Comp. Geom., Nice, 1997, pp. 119-128.
23. J. Richter-Gebert and G. Ziegler, Oriented Matroids, in [12], 1997, pp. 111-132.
24. I. Streinu, Clusters of stars, Proc. 13th ACM Symp. Comput. Geometry, Nice, 1997, pp. 439-441.