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Bruhat order of Coxeter groups and shellability. (English) Zbl 0481.06002


MSC:

06A06 Partial orders, general
05A19 Combinatorial identities, bijective combinatorics
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
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References:

[1] Björner, A., Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc., 260, 159-183 (1980) · Zbl 0441.06002
[2] Bourbaki, N., Groupes et algèbres de Lie, (Éléments de mathématique, Fasc. XXXIV (1968), Hermann: Hermann Paris), Chaps. 4, 5, and 6 · Zbl 0483.22001
[3] de Concini, C.; Lakshmibai, V., Arithmetic Cohen-Macaulayness and arithmetic normality for Schubert varieties, Amer. J. Math., 103, 835-850 (1981) · Zbl 0475.14045
[4] Danaraj, G.; Klee, V., Shellings of spheres and polytopes, Duke Math. J., 41, 443-451 (1974) · Zbl 0285.52003
[5] Deodhar, V. V., Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function, Invent. Math., 39, 187-198 (1977) · Zbl 0333.20041
[6] Edelman, P. H., The Bruhat order of the symmetric group is lexicographically shellable, (Proc. Amer. Math. Soc., 82 (1981)), 355-358 · Zbl 0478.06002
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[8] Hochster, M., Cohen-Macaulay rings, combinatorics, and simplicial complexes, (McDonald, B.; Morris, R., Proceedings, 2nd Oklahoma Ring Theory Conference (1977), Dekker: Dekker New York), 171-223 · Zbl 0351.13009
[9] R. Proctor; R. Proctor
[10] Rota, G.-C, On the foundations of Combinatorial Theory I: Theory of Möbius functions, Z. Wahrsch. Verw. Gebiete, 2, 340-368 (1964) · Zbl 0121.02406
[11] Stanley, R. P., Finite lattices and Jordan-Hölder sets, Algebra Universalis, 4, 361-371 (1974) · Zbl 0303.06006
[12] Stanley, R. P., Cohen-Macaulay complexes, (Aigner, M., Higher Combinatorics (1977), Reidel: Reidel Dordrecht/Boston), 51-62 · Zbl 0376.55007
[13] Stanley, R. P., Hilbert functions of graded algebras, Adv. in Math., 28, 57-83 (1978) · Zbl 0384.13012
[14] Verma, D.-N, Möbius inversion for the Bruhat ordering on a Weyl group, Ann. Sci. École Norm. Sup., 4, 393-398 (1971) · Zbl 0236.20035
[15] Verma, D.-N, A strengthening of the exchange property of Coxeter groups (1972), preprint
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