×

Cohen-Macaulay ordered sets. (English) Zbl 0451.06004


MSC:

06A06 Partial orders, general
06A12 Semilattices
06C10 Semimodular lattices, geometric lattices
18G99 Homological algebra in category theory, derived categories and functors
55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology
55P99 Homotopy theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Baclawski, K., Whitney numbers of geometric lattices, Advances in Math., 16, 125-138 (1975) · Zbl 0326.05027
[2] Baclawski, K., Homology and Combinatorics of Ordered Sets, (Ph.D. thesis (1976), Harvard University)
[3] Baclawski, K., Galois connections and the Leray spectral sequence, Advances in Math., 25, 191-215 (1977) · Zbl 0362.06008
[4] Baclawski, K., The Möbius algebra as a Grothendieck ring, J. Algebra, 57, 167-179 (1979) · Zbl 0407.18010
[5] Baclawski, K., Cohen-Macauley connectivity and geometric lattices (1979), Haverford College, preprint
[6] Baclawski, K.; Björner, A., Fixed points in partially ordered sets, Advances in Math., 31, 263-287 (1979) · Zbl 0417.06002
[8] Birkhoff, G., Lattice Theory, (Amer. Math. Soc. Colloq. Publ., XXV (1967), Amer. Math. Soc: Amer. Math. Soc Providence, R. I) · Zbl 0126.03801
[11] Bruggesser, H.; Mani, P., Shellable decompositions of cells and spheres, Math. Scand., 29, 197-205 (1971) · Zbl 0251.52013
[12] Cartan, H.; Eilenberg, S., Homological Algebra (1956), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J · Zbl 0075.24305
[13] Crapo, H., The Möbius function of a lattice, J. Combinatorial Theory, 1, 126-131 (1966) · Zbl 0146.01601
[14] Danaraj, G.; Klee, V., Which spheres are shellable?, Ann. Discrete Math., 2, 33-52 (1978) · Zbl 0401.57031
[16] Folkman, J., The homology groups of a lattice, J. Math. Mech., 15, 631-636 (1966) · Zbl 0146.01602
[17] Garsia, A., Méthodes combinatoires dans la théorie des anneaux de Cohen-Macauley, C. R. Acad. Sci. Paris Sér. A, 288, 371-374 (1979) · Zbl 0401.13014
[19] Godement, R., Topologie algébrique et théorie des faisceaux (1958), Hermann et Cie: Hermann et Cie Paris · Zbl 0080.16201
[20] Hartshorne, R., Local Cohomology, (Lectures Notes in Mathematics, No. 41 (1967), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0176.18303
[21] Hochster, M., Cohen-Macaulay rings, combinatorics and simplicial complexes, (Proc. Second Oklahoma Ring Theory Conf.. Proc. Second Oklahoma Ring Theory Conf., March, 1976 (1977), Dekker: Dekker New York) · Zbl 0351.13009
[22] Kempf, G., The Grothendieck-Cousin complex of an induced representations, Advances in Math., 29, 310-396 (1978) · Zbl 0393.20027
[23] McMullen, P.; Shephard, G., Convex Polytopes and the Upper Bound Conjecture, (London Math Soc. Lecture Note Ser. 3 (1971), Cambridge Univ. Press: Cambridge Univ. Press London/New York) · Zbl 0217.46702
[24] Munkres, J., Topological results in combinatorics (1977), MIT, preprint
[25] Quillen, D., Homotopy properties of the poset of non-trivial \(p\)-subgroups of a group, Advances in Math., 28, 101-128 (1978) · Zbl 0388.55007
[26] Reisner, G., Cohen-Macaulay quotients of polynomial rings, Advances in Math., 21, 30-49 (1976) · Zbl 0345.13017
[27] Rota, G.-C, On the foundations of combinatorial theory. I. Theory of Möbius functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 2, 340-368 (1964) · Zbl 0121.02406
[28] Rota, G.-C, On the combinatorics of the Euler characteristic, Studies in Pure Math., 221-233 (1971), (Rado Festschrift issue)
[29] Rudin, M. E., An unshellable triangulation of a tetrahedron, Bull. Amer. Math. Soc., 64, 90-91 (1958) · Zbl 0082.37602
[30] Spanier, E., Algebraic Topology (1966), McGraw-Hill: McGraw-Hill New York · Zbl 0145.43303
[31] Stanley, R., Modular elements of geometric lattices, Alg. Univ., 1, 214-217 (1971) · Zbl 0229.05032
[32] Stanley, R., Supersolvable lattices, Alg. Univ., 2, 197-217 (1972) · Zbl 0256.06002
[33] Stanley, R., Finite lattices and Jordan-Hölder sets, Alg. Univ., 4, 361-371 (1974) · Zbl 0303.06006
[34] Stanley, R., Combinatorial reciprocity theorems, Advances in Math., 14, 194-253 (1974) · Zbl 0294.05006
[35] Stanley, R., The upper bound conjecture and Cohen-Macaulay rings, Studies in Appl. Math., 54, 135-142 (1975) · Zbl 0308.52009
[36] Stanley, R., Cohen-Macaulay complexes, (Aigner, M., Higher Combinatorics (1977), NATO Advanced Study Institutes Series: NATO Advanced Study Institutes Series Reidel, Dordrecht), 51-62
[37] Stanley, R., Balanced Cohen-Macaulay complexes, Trans. Amer. Math. Soc., 249, 139-157 (1979) · Zbl 0411.05012
[38] Tutte, W. T., A homotopy theorem for matroids, I, II, Trans. Amer. Math. Soc., 88, 144-174 (1958) · Zbl 0081.17301
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.