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Sufficiently of McMullen’s conditions for f-vectors of simplicial polytopes. (English) Zbl 0431.52009

MSC:
52Bxx Polytopes and polyhedra
05A19 Combinatorial identities, bijective combinatorics
05A15 Exact enumeration problems, generating functions
90C05 Linear programming
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[1] Branko Grünbaum, Convex polytopes, With the cooperation of Victor Klee, M. A. Perles and G. C. Shephard. Pure and Applied Mathematics, Vol. 16, Interscience Publishers John Wiley & Sons, Inc., New York, 1967. · Zbl 0152.20602
[2] Nathan Jacobson, Lectures in abstract algebra. Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964. · Zbl 0124.27002
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[4] Victor Klee, Convex polyhedra and mathematical programming, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 485 – 490. · Zbl 0334.52008
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[7] P. McMullen and D. W. Walkup, A generalized lower-bound conjecture for simplicial polytopes, Mathematika 18 (1971), 264 – 273. · Zbl 0233.52003 · doi:10.1112/S0025579300005520 · doi.org
[8] Richard P. Stanley, The upper bound conjecture and Cohen-Macaulay rings, Studies in Appl. Math. 54 (1975), no. 2, 135 – 142. · Zbl 0308.52009
[9] Richard P. Stanley, Cohen-Macaulay complexes, Higher combinatorics (Proc. NATO Advanced Study Inst., Berlin, 1976), Reidel, Dordrecht, 1977, pp. 51 – 62. NATO Adv. Study Inst. Ser., Ser. C: Math. and Phys. Sci., 31.
[10] Richard P. Stanley, Hilbert functions of graded algebras, Advances in Math. 28 (1978), no. 1, 57 – 83. · Zbl 0384.13012 · doi:10.1016/0001-8708(78)90045-2 · doi.org
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