Methods for Constructing Shellable Simplicial Complexes

A clutter C with vertex set X is an antichain of 2X such that X = [C. For any clutter C, we consider the independence complex of C whose faces are independent sets in C. In this paper, we introduce some methods to obtain clutters C Œ containing a given clutter C as an induced subclutter such that the independence complex of C Œ is shellable. Consequently, for a given squarefree monomial ideal I S = K[x1; : : : ; xn], we obtain a squarefree monomial ideal J I in an extension ring S Œ of S such that the ring S Œ=J is Cohen-Macaulay.