Algebraic shifting and graded Betti numbers

Authors:
Satoshi Murai and Takayuki Hibi

Journal:
Trans. Amer. Math. Soc. **361** (2009), 1853-1865

MSC (2000):
Primary 13D02; Secondary 13F55

DOI:
https://doi.org/10.1090/S0002-9947-08-04707-7

Published electronically:
October 20, 2008

MathSciNet review:
2465820

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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 Stanley-Reisner 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 560-0043, Japan

Email:
s-murai@ist.osaka-u.ac.jp

**Takayuki Hibi**

Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan

Email:
hibi@math.sci.osaka-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-08-04707-7

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.