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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© 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
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