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Cohen-Macaulay Complexes

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Higher Combinatorics

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 31))

Abstract

Let Δ be a finite simplicial complex (or complex for short) on the vertex set V = (x1,…,xn). Thus, Δ is a collection of subsets of V satisfying the two conditions: (i) (xi) ε Δ for all xi ε V, and (ii) if F ε Δ and G ⊂ F, then G ε Δ. There is a certain commutative ring AΔ which is closely associated with the combinatorial and topological properties of Δ. We will discuss this association in the special case when AΔ is a Cohen-Macaulay ring. Lack of space prevents us from giving most of the proofs and from commenting on a number of interesting sidelights. However, a greatly expanded version of this paper is being planned.

Partially supported by NSF Grant # MCS 7308445-A04

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Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Richard P. Stanley

Authors
  1. Richard P. Stanley
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik, Freie Universität Berlin, Königin-Luise-Strasse 24/26, D-1000, Berlin 33, Germany

    Martin Aigner

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© 1977 D. Reidel Publishing Company, Dordrecht-Holland

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Stanley, R.P. (1977). Cohen-Macaulay Complexes. In: Aigner, M. (eds) Higher Combinatorics. NATO Advanced Study Institutes Series, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1220-1_3

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  • DOI: https://doi.org/10.1007/978-94-010-1220-1_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1222-5

  • Online ISBN: 978-94-010-1220-1

  • eBook Packages: Springer Book Archive

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