When will the Stanley depth increase?

Shen, Yi-Huang

doi:10.1090/S0002-9939-2013-12003-4

When will the Stanley depth increase?
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Proc. Amer. Math. Soc. 141 (2013), 2265-2274 Request permission

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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