When will the Stanley depth increase?
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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 $\operatorname {sdepth}_S(I)\ge d+1$.References
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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
- Email: yhshen@ustc.edu.cn
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2265-2274
- MSC (2010): Primary 05E45, 05E40, 06A07; Secondary 13C13, 05C70
- DOI: https://doi.org/10.1090/S0002-9939-2013-12003-4
- MathSciNet review: 3043008