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Linear Diophantine equations and local cohomology. (English) Zbl 0516.10009

11D04 Linear Diophantine equations
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
55N99 Homology and cohomology theories in algebraic topology
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
Full Text: DOI EuDML
[1] [B-G] Baclawski, K., Garsia, A.M.: Combinatorial decompositions of a class of rings. Advances in Math.39, 155-184 (1981) · Zbl 0466.13003 · doi:10.1016/0001-8708(81)90027-X
[2] [B] Björner, A.: Homotopy type of posets and lattice complementation. J. Combinatorial Theory Ser. A30, 90-100 (1981) · Zbl 0442.55011 · doi:10.1016/0097-3165(81)90042-X
[3] [B-M] Brugesser, H., Mani, P.: Shellable decompositions of cells and spheres. Math. Scand.29, 197-205 (1971)
[4] [C-S] Chomsky, N., Schützenberger, M.-P.: The algebraic theory of context-free languages. In: Computer programming and formal systems (Braffort, P., Hirschberg, D., eds.). Amsterdam: North-Holland Publications 1963
[5] [F] Folkman, J.: The homology groups of a lattice. J. Math. Mech.15, 631-636 (1966) · Zbl 0146.01602
[6] [G] Garsia, A.M.: Combinatorial methods in the theory of Cohen-Macaulay rings. Advances in Math.38, 229-266 (1980) · Zbl 0461.06002 · doi:10.1016/0001-8708(80)90006-7
[7] [G-W] Goto, S., Watanabe, K.: On graded rings. II. (Z n-graded rings). Tokyo J. Math.1, 237-261 (1978) · Zbl 0406.13007 · doi:10.3836/tjm/1270216496
[8] [G-Y] Grace, J.H., Young, A.: The Algebra of Invariants. Cambridge: Cambridge University Press 1903; reprinted by New York: Stechert 1941 · JFM 34.0114.01
[9] [H-K] Herzog, J., Kunz, E. (eds.): Der kanonische Modul eines Cohen-Macaulay-Rings. Lecture Notes in Math. vol. 238. Berlin-Heidelberg-New York: Springer 1971
[10] [H] Hochster, M.: Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes. Ann. of Math.96, 318-337 (1972) · Zbl 0237.14019 · doi:10.2307/1970791
[11] [H-R] Hochster, M., Roberts, J.L.: Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay. Advances in Math.13, 115-175 (1974) · Zbl 0289.14010 · doi:10.1016/0001-8708(74)90067-X
[12] [L] Lakser, H.: The homology of a lattice. Discrete Math.1, 187-192 (1971) · Zbl 0227.06002 · doi:10.1016/0012-365X(71)90024-0
[13] [M-S] McMullen, P., Shephard, G.C.: Convex polytopes and the upper bound conjecture. London Math. Soc. Lecture Note Series, vol. 3. Cambridge: Cambridge University Press 1971 · Zbl 0217.46702
[14] [M] Mumford, D.: Hilbert’s fourteenth problem-the finite generation of subrings such as rings of invariants. In: Mathematical developments arising from Hilbert problems (Browder, F., ed.). Proc. Symposia Pure Math., vol. 28, pp. 431-444. Providence, R.I.: American Mathematical Society 1976 · Zbl 0341.14019
[15] [Sp] Spanier, E.H.: Algebraic Topology. New York: McGraw-Hill 1966 · Zbl 0145.43303
[16] [St1] Stanley, R.: Linear homogeneous diophantine equations and magic labelings of graphs. Duke Math. J.40, 607-632 (1973) · Zbl 0269.05109 · doi:10.1215/S0012-7094-73-04054-4
[17] [St2] Stanley, R.: Combinatorial reciprocity theorems. Advances in Math.14, 194-253 (1974) · Zbl 0294.05006 · doi:10.1016/0001-8708(74)90030-9
[18] [St3] Stanley, R.: Hilbert functions of graded algebras. Advances in Math.38, 57-83 (1978) · Zbl 0384.13012 · doi:10.1016/0001-8708(78)90045-2
[19] [St4] Stanley, R.: Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. (new series)1, 475-511 (1979) · Zbl 0497.20002 · doi:10.1090/S0273-0979-1979-14597-X
[20] [St5] Stanley, R.: Combinatorics and invariant theory. In: Relations between combinatorics and other parts of mathematics (Ray-Chaudhuri, D.K., ed.). Proc. Symposia in Pure Math., vol. 34, pp. 345-355. Providence, R.I.: American Mathematicals Society 1979
[21] [St6] Stanley, R.: Balanced Cohen-Macaulay complexes. Trans. Amer. Math. Soc.249, 139-157 (1979) · Zbl 0411.05012 · doi:10.1090/S0002-9947-1979-0526314-6
[22] [St7] Stanley, R.: Decompositions of rational convex polytopes. Annals of Discrete Math.6, 333-342 (1980) · Zbl 0812.52012 · doi:10.1016/S0167-5060(08)70717-9
[23] [St8] Stanley, R.: Interactions between commutative algebra and combinatorics. Report. U. Stockholm, 1982-No. 4
[24] [W] Walker, J.: Topology and combinatorics of ordered sets. Thesis, M.I.T., 1981
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