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The homotopy type of hyperplane posets

Authors: Paul H. Edelman and James W. Walker
Journal: Proc. Amer. Math. Soc. 94 (1985), 221-225
MSC: Primary 52A25; Secondary 06A10, 51M20, 55P10, 57Q99
MathSciNet review: 784167
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Abstract: Previously, Edelman had defined a partial order on the regions of a euclidean space dissected by hyperplanes. The goal of this paper is to compute the homotopy type of open intervals in these posets. Techniques from the theory of shellable posets are used.

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

  • [Bj1] A. Björner, Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc. 260 (1980), 159-183. MR 570784 (81i:06001)
  • [Bj2] -, Orderings of Coxeter groups, Contemporary Mathematics, vol. 34 (edited by C. Greene), Amer. Math. Soc., Providence, R. I., 1984. MR 777701 (86i:05024)
  • [BM] H. Brugesser and P. Mani, Shellable decompositions of cells and spheres, Math. Scand. 29 (1971), 197-205. MR 0328944 (48:7286)
  • [BW] A. Björner and M. Wachs, On lexicographically shellable posets, Trans. Amer. Math. Soc. 277 (1983), 323-341. MR 690055 (84f:06004)
  • [Co] R. Cordovil, A combinatorial perspective on the non-Radon partition, J. Combin. Theory Ser. A (to appear). MR 773553 (87e:52003a)
  • [Ed] P. H. Edelman, A partial order on the regions of $ {{\mathbf{R}}^n}$ dissected by hyperplanes, Trans. Amer. Math. Soc. 283 (1984), 617-631. MR 737888 (85k:51030)
  • [Pr] J. S. Provan, Decompositions, shellings, and diameters of simplicial complexes and convex polyhedra, Cornell Univ. School of Operations Research and Industrial Engineering, Technical Report No. 354, 1977.
  • [Qu] D. Quillen, Homotopy properties of the poset of nontrivial $ p$-subgroups of a group, Adv. in Math. 28 (1978), 101-128. MR 493916 (80k:20049)
  • [Wa] J. W. Walker, Homotopy type and Euler characteristic of partially ordered sets, European J. Combin. 2 (1981), 373-384. MR 638413 (83g:06002)

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Keywords: Dissection by hyperplanes, shellability, homotopy type, Möbius function
Article copyright: © Copyright 1985 American Mathematical Society

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