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IPM
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“School of Mathematics”

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Paper   IPM / M / 14987
School of Mathematics
  Title:   Homological invariants of the Stanley-Reisner ring of a k-decomposable simplicial complex
  Author(s):  Somayeh Moradi
  Status:   To Appear
  Journal: Asian-European Journal of Mathematics (AEJM)
  Supported by:  IPM
  Abstract:
In this paper we study the regularity and the projective dimension‎ ‎of the Stanley-Reisner ring of a k-decomposable simplicial complex and explain these invariants with a recursive formula‎. ‎To this aim‎, ‎the graded Betti numbers of decomposable monomial ideals which is the dual concept‎ ‎for k-decomposable simplicial complexes are studied and an inductive formula for the Betti numbers is given‎. ‎As a corollary‎, ‎for a shellable simplicial complex ∆‎, ‎a formula for the regularity of the Stanley-Reisner ring of ∆ is presented‎. ‎Finally‎, ‎for a chordal clutter H‎, ‎an upper bound for \Treg(I(H)) is given in terms of the regularities of edge ideals of some chordal clutters which are minors of H‎.

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