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 When will the Stanley depth increase


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Let $I\subset S=\KKx 1,

.,x n$ be an ideal generated by squarefree monomials of degree $\ge d$. If the number of degree $d$ minimal generating monomials $\mu dI\le \min\binom{n}{d+1},\sum {j=1}^{n-d}\binom{2j-1}{j}$, then the Stanley depth $\sdepth SI\ge d+1$.



Author: Yi-Huang Shen

Source: https://archive.org/



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