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- W2060185552 abstract "If a pure simplicial complex is partitionable, then its h-vector has a combinatorial interpretation in terms of any partitioning of the complex. Given a non-partitionable complex Δ, we construct a complex Γ⊇Δ of the same dimension such that both Γ and the relative complex (Γ,Δ) are partitionable. This allows us to rewrite the h-vector of any pure simplicial complex as the difference of two h-vectors of partitionable complexes, giving an analogous interpretation of the h-vector of a non-partitionable complex.By contrast, for a given complex Δ it is not always possible to find a complex Γ such that both Γ and (Γ,Δ) are Cohen–Macaulay. We characterize when this is possible, and we show that the construction of such a Γ in this case is remarkably straightforward. We end with a note on a similar notion for shellability and a connection to Simon’s conjecture on extendable shellability for uniform matroids." @default.
- W2060185552 created "2016-06-24" @default.
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- W2060185552 date "1976-07-01" @default.
- W2060185552 modified "2023-09-30" @default.
- W2060185552 title "Cohen-Macaulay quotients of polynomial rings" @default.
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- W2060185552 doi "https://doi.org/10.1016/0001-8708(76)90114-6" @default.
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