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| Paper IPM / M / 14987 |
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| Abstract: | |
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In this paper we study the regularity and the projective dimensionâ
âof the Stanley-Reisner ring of a k-decomposable 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 k-decomposable 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 Stanley-Reisner 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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