On the Behaviour of Stanley Depth under Variable Adjunction

Abstract

Let $S=K[x_1,...,x_n]$ be a polynomial ring in $n$ variables over the field $K$. For integers $1\le t<n$ consider the ideal $I=(x_1,...,x_t)\cap (x_{t+1},...,x_n)$ in $S$. In this paper we bound from above the Stanley depth of the ideal $I^{\prime }=(I,x_{n+1},...,x_{n+p})\subset S^{\prime }=S[x_{n+1},...,x_{n+p}]$. We give similar upper bounds for the Stanley depth of the ideal $(I_{n,2},x_{n+1},...,x_{n+p})$, where $I_{n,2}$ is the square free Veronese ideal of degree 2 in $n$ variables.

References in corpus (2)

• Stanley Decompositions, Pretty Clean Filtrations and Reductions Modulo Regular Elements
• Upper bounds for the Stanley depth

Cited by in corpus (2)

• Values and bounds of the Stanley depth
• Stanley depth of edge ideals