Algebraic shifting and graded Betti numbers
Authors:
Satoshi Murai and Takayuki Hibi
Journal:
Trans. Amer. Math. Soc. 361 (2009), 18531865
MSC (2000):
Primary 13D02; Secondary 13F55
Published electronically:
October 20, 2008
MathSciNet review:
2465820
Fulltext PDF Free Access
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Abstract: Let denote the polynomial ring in variables over a field with each . Let be a simplicial complex on and its StanleyReisner ideal. We write for the exterior algebraic shifted complex of and for a combinatorial shifted complex of . Let denote the graded Betti numbers of . In the present paper it will be proved that (i) for all and , where the base field is infinite, and (ii) for all and , where the base field is arbitrary. Thus in particular one has for all and , where is the unique lexsegment simplicial complex with the same vector as and where the base field is arbitrary.
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Additional Information
Satoshi Murai
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 5600043, Japan
Email:
smurai@ist.osakau.ac.jp
Takayuki Hibi
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 5600043, Japan
Email:
hibi@math.sci.osakau.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002994708047077
PII:
S 00029947(08)047077
Received by editor(s):
March 2, 2007
Published electronically:
October 20, 2008
Article copyright:
© Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
