Mihai Cipu and Muhammad Imran Qureshi: On the behaviour of Stanley depth under variable adjunction. p.129-146

Abstract:

Let $S=K[x_1,\ldots,x_n]$ be a polynomial ring in $n$ variables over the field $K$. For integers $1\leq t< n$ consider the ideal $I=(x_1,\ldots,x_t)\cap(x_{t+1}, \ldots,x_n)$ in $S$. In this paper we bound from above the Stanley depth of the ideal $I'=(I,x_{n+1},\ldots,x_{n+p})\subset S'=S[x_{n+1},\ldots,x_{n+p}]$. We give similar upper bounds for the Stanley depth of the ideal $(I_{n,2},x_{n+1},\ldots,x_{n+p})$, where $I_{n,2}$ is the squarefree Veronese ideal of degree 2 in $n$ variables.

Key Words: monomial ideals; Stanley decompositions; Stanley depth; squarefree Veronese ideals.

2000 Mathematics Subject Classification: Primary: 05E40;
Secondary: 06A07; 13C13; 13P10.

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