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Oriented Matroids: The Power of Unification


6. References

Aichholzer, O. and F. Aurenhammer, H. Krasser, Enumerating order types for small point sets with applications, Proc. 17th Annual ACM Symposium on Computational Geometry, New York, 2001, p. 11-18.

Aichholzer, O. and F. Aurenhammer, H. Krasser, Points and Combinatorics, preprint.

Aigner, M. and G. Ziegler, Proofs from The Book, 2nd. edition, Springer-Verlag, New York, 2001.

Begehr, H. and H. Koch, J. Kramer, N. Schappacher, E.-J. Thiele, (eds.), Mathematics in Berlin, Birkhäuser, Berlin, 1998.

Begehr , H., (ed.), Mathematik in Berlin, Geschichte und Dokumentation, Erster Halbband. Shaker Verlag, Aachen, 1998

Björner, A. and M. Las Vergnas, B. Sturmfels, N. White, G. Ziegler, Oriented Matroids, 2nd. ed., Cambridge U. Press, New York, 1999.

Bohne, J., Eine kombinatorische Analyse zonotopaler Raumaufteilungen, Dissertation, U. Bielefeld, 1992.

Cordovil, R., Orient matroids of rank three and arrangements of pseudolines, Combinatorial Mathematics, North-Holland Math. Stud. 75, North-Holland, Amsterdam, 1983, p. 219-223.

Dress, A., Chirotopes and oriented matroids, Bayreuther Math. Schriften, 21 (1986) 14-68.

Felsner, S., On the number of arrangements of pseudolines, Discrete Comput. Geometry, 18 (1997) 257-267.

Felsner, S., and F. Hurtado, M. Noy, I. Streinu, Hamiltonicity and colorings of arrangement graphs, Proc. of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, 2000, p. 155-164.

Felsner, S. and K. Kriegel, Triangles in Euclidean arrangements, Discrete Comput. Geom., 22 (1999) 429-438.

Felsner, S. and H. Weil, Sweeps, arrangements and signotopes, Discrete Appl. Math., 109 (2001) 67-94.

Felsner, S. and G. Ziegler, Zonotopes associated with higher Bruhat orders, Discrete Math. 241 (2001) 301-312.

Felsner, S. and K. Kriegel, Triangles in Euclidean arrangements.

Finshi, L., A Graph Theoretical Approach for Reconstruction and Generation of Oriented Matroids, Ph. D. Thesis, Swiss Federal Institute of Technology, 2001.

Gavril, F. and J. Schönheim, Characterizations and algorithms of curve map graphs, Discrete Applied Math., 4 (1982) 181-191.

Goodman, J., Proof of a conjecture of Burr, Grünbaum, and Sloane, Discrete Math., 32 (1980) 27-35,

Goodman, J., Pseudoline arrangements, In Handbook of Discrete and Computational Geometry, J. Goodman and J. O'Rourke, (eds.), CRC Press, Boca Raton, 1997, p. 83-109.

Goodman, J. and R. Pollack, Proof of Grünbaum's conjecture on the stretchability of certain arrangements of pseudolines, J. Comb. Theory A, 29 (1980) 385-390.

Goodman, J. and R. Pollack, On the combinatorial classification of nondegenerate configurations in the plane, J. Combin. Theory Ser. A, 29 (1980) 220-225.

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Goodman, J. and R. Pollack, Allowable sequences and order types in discrete and computational geometry, in New Trends in Discrete and Computational Geometry, Janos Pach (ed.), Springer-Verlag, New York, 1993, p. 103-134.

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Goodman, J. and J. O'Rourke (eds.), Handbook of Discrete and Computational Geometry, CRC Press, Boca Raton, 1997.

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Grünbaum, B., Arrangements and Spreads, Regional Conference Series in Mathematics, Volume 10, American Mathematical Society, Providence, 1972.

Harborth, H., Some simple arrangements of pseudolines with a maximum number of triangles, in Discrete Geometry and Convexity, J. Goodman, et al. (eds.), Volume 440, Annals of the New York Academy of Sciences, New York, 1985, p. 31-33.

Jamison, R. A survey of the slope problem, in Discrete Geometry and Convexity, J. Goodman, E. Lutwak, J. Malkevitch, R. Pollack, (eds.), Annals of the New York Academy of Sciences, Volume 440, p. 34--51.
Jamison, R. and D. Hill, A catalogue of slope-critical configurations, Congressus Numerantium, 40 (1983) 101-125.

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Penne, Configurations of few lines in 3-space. Isotopy, chirality, and planar layouts, Geom. Ded., 45 (1993) 49-82.

Richter-Gebert, J., New construction methods for oriented matroids, Dissertation, KTH Stockholm, 1992.

Richter-Gebert, J., Combinatorial obstructions to the lifting of weaving diagrams, Discrete Comput. Geometry, 10 (1993) 287-312,

Richter-Gebert, J., Two interesting oriented matroids, Documenta Math., 1 (1996) 137-148.

Richter-Gebert, J., Realization Spaces of Polytopes, Lecture Notes in Mathematics, Volume 1643, Springer-Verlag, Berlin, 1996.

Richter-Gebert, J. and G. Ziegler, Oriented Matroids, In Handbook of Discrete and Computational Geometry, J. Goodman and J. O'Rourke, (eds.), CRC Press, Boca Raton, 1997, p. 111-132.

Ringel, G., Teilungen der Ebene durch Geraden oder Topologische Geraden, Math. Z., 64 (1956) 79-102.

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Roundneff, J.-P., The maximum number of triangles in arrangements of (pseudo-) lines, J. Combnin. Theory Ser. B, 66 (196) 44-74.

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Shor, P., Stretchability of pseudolines is NP-hard, In Applied Geometry and Discrete Mathematics- The Victor Klee Festschrift, P. Gritzmann and B. Sturmfels, (eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Amer. Math. Society, Providence, 1991, p. 531-554.

Tamaki, H. and T. Tokuyama, How to cut pseudoparabolas into segments, Discrete Comput. Geom., 19 (1998) 265-290.

Ungar, P., 2N noncollinear points determine at least 2N directions, J. Combin. Theory Ser A, 33 (1982) 343-347.

Ziegler, G., Lectures on Polytopes, Springer-Verlag, New York, 1994.

Ziegler, G.,. Oriented Matroids Today. (Available on-line.)

Those who can access JSTOR can find some of the papers mentioned above there.


  1. Introduction
  2. Digraphs and oriented matroids
  3. Arrangements of lines
  4. Arrangements of pseudolines
  5. Allowable sequences
  6. References

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