Combinatorial Shifting and Graded Betti Numbers

نویسندگان

  • SATOSHI MURAI
  • TAKAYUKI HIBI
چکیده

Let ∆ be a simplicial complex and I∆ its Stanley–Reisner ideal. It has been conjectured that, for each i and j, the graded Betti number βii+j(I∆) of I∆ is smaller than or equal to that of I∆c , where ∆ c is a combinatorial shifted complex of ∆. In the present paper the conjecture will be proved affirmatively. In particular the inequalities βii+j(I∆) ≤ βii+j(I∆lex) hold for all i and j, where ∆ is the unique lexsegment simplicial complex with the same f -vector as ∆ and where the base field is of arbitrary characteristic.

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تاریخ انتشار 2008