On the Hilbert depth of a special class of squarefree monomial ideals

2026/07/13 by Andreea I. Bordianu, Mircea Cimpoeas
#math.AC

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Abstract

Let r and n be two positive integers and S=K[x₁,…,x_n+r-1], the ring of polynomials in n+r-1 variable, over a field K. We consider the squarefree monomial ideal I_n,r:= x₁ ⋯ x_r-1 (x_r,…,x_r+n-1) ⊂ S and we prove several results regarding the Hilbert depth of S/I_n,r. Also, we consider the special case n=r.

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