Given the f-vector f = (f 0, f 1, . . .) of a Cohen-Macaulay simplicial complex, it will be proved that there exists a shellable simplicial complex Δ f with f(Δ f ) = f such that, for any Cohen-Macaulay simplicial complex Δ with f(Δ) = f, one has βi(Δ ≤ βi I Δ_ for all i and j, where f(Δ) is the f-vector of Δ and where β ij (I Δ) are graded Betti numbers of the Stanley-Reisner ideal I Δ of Δ.
- Cohen-Macaulay simplicial complex
- Graded Betti number
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