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Union and glueing of a family of Cohen-Macaulay partially ordered sets

Published online by Cambridge University Press:  22 January 2016

Takayuki Hibi
Takayuki Hibi*
Affiliation:
Department of Mathematics, Faculty of Science Nagoya University, Chikusa-ku, Nagoya, 464 Japan
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Summary

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By means of simple exact sequences in commutative algebra, we can derive some effective criteria for Cohen-Macaulay property of finite partially ordered sets.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 107 , September 1987 , pp. 91 - 119
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

[1] Baclawski, K., “Homology and combinatorics of ordered sets”, Thesis, Harvard University, 1976.Google Scholar
[2] Baclawski, K., Cohen-Macaulay ordered sets, J. Algebra, 63 (1980), 226–258.CrossRefGoogle Scholar
[3] Baclawski, K., Cohen-Macaulay connectivity and geometric lattices, European J. Comb., 3 (1982), 293–305.CrossRefGoogle Scholar
[4] Baclawski, K. and Garsia, A., Combinatorial decompositions of a class of rings, Adv. in Math., 39 (1981), 155–184.CrossRefGoogle Scholar
[5] Birkhoff, G., “Lattice Theory”, 3rd. ed., Amer. Math. Soc. Colloq. Publ., No. 25, Amer. Math. Soc, Providence, R.I., 1967.Google Scholar
[6] Björner, A., Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc, 260 (1980), 159–183.CrossRefGoogle Scholar
[7] Björner, A., Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings, Adv. in Math., 52 (1984), 173–212.CrossRefGoogle Scholar
[8] Björner, A. and Wachs, M., On lexicographically shellable posets, Trans. Amer. Math. Soc, 277 (1983), 323–341.CrossRefGoogle Scholar
[9] Bruggesser, H. and Mani, P., Shellable decompositions of cells and spheres, Math. Scand., 29 (1971), 197–205.CrossRefGoogle Scholar
[10] Concini, C. De, Eisenbud, D. and Procesi, C., Hodge Algebras, Astérisque, 91 (1982).Google Scholar
[11] Folkman, J., The homology groups of a lattice, J. Math. Mech., 15 (1966), 631–636.Google Scholar
[12] Garsia, A., Combinatorial methods in the theory of Cohen-Macaulay rings, Adv. in Math., 38 (1980), 229–266.CrossRefGoogle Scholar
[13] Gilmore, P. and Hoffmann, A. J., A characterization of comparability graphs and interval graphs, Canad. J. Math., 16 (1967), 539–548.CrossRefGoogle Scholar
[14] Goto, S. and Watanabe, K.-i., On graded rings, I, J. Math. Soc. Japan, 30 (1978), 179–213.CrossRefGoogle Scholar
[15] Hibi, T., Distributive lattices, affine semigroup rings and algebras with straightening laws, to appear in the proceeding of USA-JAPAN joint seminar on Commutative Algebra and Combinatorics held at Kyoto (August, 1985).Google Scholar
[16] Hibi, T., Level rings and algebras with straightening laws, to appear.Google Scholar
[17] Hibi, T. and Watanabe, K.-i., Study of three-dimensional algebras with straightening laws which are Gorenstein domains I, Hiroshima Math. J., 15 (1985), 27–54.Google Scholar
[18] Hibi, T. and Watanabe, K.-i., Study of three-dimensional algebras with straightening laws which are Gorenstein domains II, Hiroshima Math. J., 15 (1985), 321–340.Google Scholar
[19] Hochster, M., Rings of invariants of tori, Cohen-Macaulay rings generated by monomials, and polytopes, Ann. of Math., 96 (1972), 318–337.CrossRefGoogle Scholar
[20] Hochster, M., Cohen-Macaulay rings, combinatorics and simplicial complexes, Ring Theory II, Proc. Second Oklahoma Conf. (March, 1976), Lect. Notes in Pure and Appl. Math., No. 26, Dekker, 1977, 171–223.Google Scholar
[21] Kind, B. and Kleinschmidt, P., Schälbara Cohen-Macaulay Komplexe und ihre Parametrisierung, Math. Z., 167 (1979), 173–179.CrossRefGoogle Scholar
[22] McMullen, P., The maximal number of faces of a convex polytope, Mathematika, 17 (1970), 179–184.CrossRefGoogle Scholar
[23] Munkres, J., Topological results in combinatorics, Michigan Math. J., 31 (1984), 113–128.CrossRefGoogle Scholar
[24] Reisner, G., Cohen-Macaulay quotients of polynomial rings, Adv. in Math., 21 (1976), 30–49.CrossRefGoogle Scholar
[25] Schenzel, P., On the number of faces of simplicial complexes and the purity of Frobenius, Math. Z., 178 (1981), 125–142.CrossRefGoogle Scholar
[26] Stanley, R., The upper bound conjecture and Cohen-Macaulay rings, Studies in Appl. Math., 54 (1975), 135–142.CrossRefGoogle Scholar
[27] Stanley, R., Cohen-Macaulay complexes, Higher Combinatorics (M. Aigner, editor), NATO Advanced Study Institute Series, Reidel, Dordrecht and Boston, 1977, 51–62.Google Scholar
[28] Stanley, R., Hilbert functions of graded algebras, Adv. in Math., 28 (1978), 57–83.CrossRefGoogle Scholar
[29] Stanley, R., Balanced Cohen-Macaulay complexes, Trans. Amer. Math. Soc, 249 (1979), 139–157.CrossRefGoogle Scholar
[30] Stanley, R., “Combinatorics and Commutative Algebra”, Progress in Math., Vol. 41, Birkháuser, 1983.CrossRefGoogle Scholar
[31] Stückrad, J. and Vogel, W., Toward a theory of Buchsbaum singularities, Amer. J. Math., 100 (1973), 727–746.CrossRefGoogle Scholar
[32] Watanabe, K.-i., Study of algebras with straightening laws of dimension 2, Algebraic and Topological Theories—to the memory of Dr. Takehiko Miyata (Nagata, M. et al., eds.), Kinokuniya, Tokyo, 1985, 622–639.Google Scholar
[33] Ziegler, G., On the poset of partitions of an integer, J. Combin. Theory, Series A, 42 (1986),215–222.CrossRefGoogle Scholar
[34] Hibi, T., Plane graphs and Cohen-Macaulay posets, submitted.Google Scholar
[35] Hibi, T., Regular and semi-regular points of Cohen-Macaulay partially ordered sets, submitted.Google Scholar
[36] Hibi, T., Canonical ideals of Cohen-Macaulay partially ordered sets, to appear.Google Scholar