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When will the Stanley depth increase?

Author: Yi-Huang Shen
Journal: Proc. Amer. Math. Soc. 141 (2013), 2265-2274
MSC (2010): Primary 05E45, 05E40, 06A07; Secondary 13C13, 05C70
Published electronically: March 20, 2013
MathSciNet review: 3043008
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Abstract: Let $ I\subset S=\mathbb{K},[x_1,\dots ,x_n]$ be an ideal generated by squarefree monomials of degree $ \ge d$. If the number of degree $ d$ minimal generating monomials is $ \mu _d(I)\le \min (\binom {n}{d+1},\sum _{j=1}^{n-d}\binom {2j-1}{j})$, then the Stanley depth $ \operatorname {sdepth}_S(I)\ge d+1$.

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Additional Information

Yi-Huang Shen
Affiliation: The Wu Wen-Tsun Key Laboratory of Mathematics of CAS and School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China

Keywords: Stanley depth, squarefree monomial ideal
Received by editor(s): October 18, 2011
Published electronically: March 20, 2013
Additional Notes: This work was supported by the National Natural Science Foundation of China (11201445) and the Fundamental Research Funds for the Central Universities (WK0010000017).
Communicated by: Irena Peeva
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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