The Behavior of Graded Betti Numbers via Algebraic Shifting and Combinatorial Shifting
نویسندگان
چکیده
Let ∆ be a simplicial complex and I∆ its Stanley–Reisner ideal. We write ∆ for the exterior algebraic shifted complex of ∆ and ∆ for a combinatorial shifted complex of ∆. It will be proved that for all i and j one has the inequalities βii+j(I∆e) ≤ βii+j(I∆c) on the graded Betti numbers of I∆e and I∆c . In addition, the bad behavior of graded Betti numbers of I∆c will be studied.
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Shifting Operations and Graded Betti Numbers
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