On the Behaviour of Stanley Depth under Variable Adjunction

2010/07/20 by Mihai Cipu, Cipu, Mihai, Muhammad Imran Qureshi +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1007.3340

openalex publication_date 2010/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S=K[x₁,...,x_n] be a polynomial ring in n variables over the field K. For integers 1≤ t< n consider the ideal I=(x₁,...,x_t)∩(x_t+1, ...,x_n) in S. In this paper we bound from above the Stanley depth of the ideal I'=(I,x_n+1,...,x_n+p)⊂ S'=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.

Citations

• Stanley Decompositions, Pretty Clean Filtrations and Reductions Modulo Regular Elements

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