The Bruhat order of the symmetric group is lexicographically shellable

Edelman, Paul H.

doi:10.1090/S0002-9939-1981-0612718-4

The Bruhat order of the symmetric group is lexicographically shellable
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Proc. Amer. Math. Soc. 82 (1981), 355-358 Request permission

Abstract:

The title theorem is proven. It then follows from a theorem of Björner that the simplicial complex of chains of this Bruhat order is shellable and thus Cohen-Macaulay. It is further established that this complex is a double cone over a triangulation of a sphere.

References

Kenneth Baclawski, Cohen-Macaulay ordered sets, J. Algebra 63 (1980), no. 1, 226–258. MR 568572, DOI 10.1016/0021-8693(80)90033-2
Anders Björner, Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc. 260 (1980), no. 1, 159–183. MR 570784, DOI 10.1090/S0002-9947-1980-0570784-2
Gopal Danaraj and Victor Klee, Shellings of spheres and polytopes, Duke Math. J. 41 (1974), 443–451. MR 345113
Gopal Danaraj and Victor Klee, Which spheres are shellable?, Ann. Discrete Math. 2 (1978), 33–52. MR 500687

Classical Bruhat orders are lexicographically shellable

Richard P. Stanley, Cohen-Macaulay complexes, Higher combinatorics (Proc. NATO Advanced Study Inst., Berlin, 1976) NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., vol. 31, Reidel, Dordrecht, 1977, pp. 51–62. MR 0572989
Daya-Nand Verma, Möbius inversion for the Bruhat ordering on a Weyl group, Ann. Sci. École Norm. Sup. (4) 4 (1971), 393–398. MR 291045