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Paper IPM / M / 14987  


Abstract:  
In this paper we study the regularity and the projective dimensionâ
âof the StanleyReisner ring of a kdecomposable simplicial complex and explain these invariants with a recursive formulaâ.
âTo this aimâ, âthe graded Betti numbers of decomposable monomial ideals which is the dual conceptâ
âfor kdecomposable simplicial complexes are studied and an inductive formula for the Betti numbers is givenâ.
âAs a corollaryâ, âfor a shellable simplicial complex ∆â,
âa formula for the regularity of the StanleyReisner ring of ∆ is presentedâ. âFinallyâ, âfor a chordal clutter Hâ, âan upper bound for \Treg(I(H)) is given in terms of the regularities of edge ideals of some chordal clutters which are minors of Hâ.
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