Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



On the decidability of Diophantine problems in combinatorial geometry

Author: Bernd Sturmfels
Journal: Bull. Amer. Math. Soc. 17 (1987), 121-124
MSC (1985): Primary 52A25, 05B35; Secondary 11U05
MathSciNet review: 888886
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. A. Bachem, Convexity and optimization in discrete structures, Convexity and Applications (P. M. Gruber and J. Wills, eds.), Birkhäuser, Basel, 1983. MR 731104
  • 2. L. J. Billera and B. S. Munson, Polarity and inner products in oriented matroids, European J. Combin. 5 (1984), 293-308. MR 782051
  • 3. J. Bokowski and B. Sturmfels, On the coordinatization of oriented matroids, Discrete and Computational Geometry 1 (1986), 293-306. MR 866365
  • 4. J. Bokowski and B. Sturmfels, Polytopal and nonpolytopal spheres-an algorithmic approach, Israel J. Math, (to appear). MR 889977
  • 5. B. Grünbaum, Convex polytopes, Interscience, London, 1967. MR 226496
  • 6. B. Grünbaum, Arrangements and spreads, CBMS Regional Conf. Ser., no. 10, Amer. Math. Soc. Providence, R.I., 1972. MR 307027
  • 7. W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry, Cambridge Univ. Press, Cambridge, 1947. MR 28055
  • 8. V. Klee and S. Wagon, Unsolved problems in mathematics (in preparation).
  • 9. Y. V. Matiyasevic, Diophantine representation of enumerable predicates, Izv. Akad. Nauk SSSR 35 (1971), 3-30. MR 274289
  • 10. B. Mazur, Arithmetic on curves, Bull. Amer. Math. Soc. (N.S.) 14 (1986), 207-259. MR 828821
  • 11. S. Mac Lane, Some interpretations of abstract linear dependence in terms of projective geometry, Amer. J. Math. 58 (1936), 236-240. MR 767094
  • 12. N. E. Mnëv, On manifolds of combinatorial types of projective configurations and convex polyhedra, Soviet. Math. Dokl. 32 (1985), 335-337.
  • 13. B. Sturmfels, Boundary complexes of convex polytopes cannot be characterized locally, J. London Math. Soc. (to appear). MR 881520
  • 14. A. Tarski, A decision method for elementary algebra and geometry, 2nd rev. ed., Univ. of California Press, Berkeley, 1951. MR 44472
  • 15. N. L. White (ed.), Theory of matroids, Cambridge Univ. Press, Cambridge, 1986.
  • 16. J. Folkman and J. Lawrence, Oriented matroids, J. Combin. Theory Ser. B 25 (1978), 199-236. MR 511992

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 52A25, 05B35, 11U05

Retrieve articles in all journals with MSC (1985): 52A25, 05B35, 11U05

Additional Information


American Mathematical Society