methods for constructing shellable simplicial complexes

A clutter c with vertex set x is an antichain of 2x such thatx = [c. for any clutter c, we consider the independence complex of c whosefaces are independent sets in c. in this paper, we introduce some methods toobtain clutters cœ containing a given clutter c as an induced subclutter suchthat the independence complex of cœ is shellable. consequently, for a givensquarefree monomial ideal i  s = k[x1; : : : ; xn], we obtain a squarefreemonomial ideal j  i in an extension ring sœ of s such that the ring sœ=j iscohen-macaulay.