Une axiomatisation au premier ordre des arrangements de pseudodroites euclidiennes

Bruno Courcelle; Frédéric Olive

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 3, page 883-903
  • ISSN: 0373-0956

Abstract

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We define a logical structure making it possible to represent arrangements of pseudolines in the Euclidean plane up to homeomorphism. We give a first-order axiomatisation of realizability of such structures by arrangements.

How to cite

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Courcelle, Bruno, and Olive, Frédéric. "Une axiomatisation au premier ordre des arrangements de pseudodroites euclidiennes." Annales de l'institut Fourier 49.3 (1999): 883-903. <http://eudml.org/doc/75368>.

@article{Courcelle1999,
abstract = {Nous définissons une structure logique permettant de représenter les classes d’homéomorphismes des arrangements de pseudodroites du plan euclidien. Nous donnons une axiomatisation finie du premier ordre de la réalisabilité des arrangements de pseudodroites.},
author = {Courcelle, Bruno, Olive, Frédéric},
journal = {Annales de l'institut Fourier},
keywords = {pseudolines; arrangements; insertions},
language = {fre},
number = {3},
pages = {883-903},
publisher = {Association des Annales de l'Institut Fourier},
title = {Une axiomatisation au premier ordre des arrangements de pseudodroites euclidiennes},
url = {http://eudml.org/doc/75368},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Courcelle, Bruno
AU - Olive, Frédéric
TI - Une axiomatisation au premier ordre des arrangements de pseudodroites euclidiennes
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 3
SP - 883
EP - 903
AB - Nous définissons une structure logique permettant de représenter les classes d’homéomorphismes des arrangements de pseudodroites du plan euclidien. Nous donnons une axiomatisation finie du premier ordre de la réalisabilité des arrangements de pseudodroites.
LA - fre
KW - pseudolines; arrangements; insertions
UR - http://eudml.org/doc/75368
ER -

References

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  4. [4] GOODMAN, Pseudoline arrangements, In J.E. Goodman and J. O'Rourke, editors, Hanbook of Discrete and Computational Geometry, pages 83-109. CRC Press LLC, 1997. Zbl0914.51007MR1730161
  5. [5] J.E. GOODMAN and R. POLLACK, Semispaces of configurations, cell complexes of arrangements, Journal of Combinatorial Theory, Series A, 37 (1984), 257-293. Zbl0551.05002MR86e:52011
  6. [6] J.E. GOODMAN, R. POLLACK, R. WENGER, and T. ZAMFIRESCU, Arrangements and topological planes, Amer. Math. Monthly, 101 (1994), 866-878. Zbl0827.51003MR95h:51026
  7. [7] B. GRUNBAUM, Arrangements and spreads. In CBMS Regional Conference, volume 10 of Series in Math. Amer. Math. Soc., Providence, R.I., 1972. Zbl0249.50011MR46 #6148
  8. [8] L. SÉGOUFIN and V. VIANU, Spacial databases via topological invariants. Proc. ACM Symp. on Principles of Databases Systems, 1998 (version finale à paraître au J. Comput. Syst. Sciences). Zbl0963.68058
  9. [9] P.W. SHOR, Stretchability of pseudolines is NP-hard. In Applied geometry and discrete mathematics, The Victor Klee Festschrift, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 4, 1991, 531-554. Zbl0751.05023MR92g:05065

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