Depth and sdepth of powers of the path ideal of a cycle graph. II
DOI:
https://doi.org/10.24193/subbmath.2025.4.01Keywords:
Stanley depth, monomial ideal, cycle graphAbstract
Let \(J_{n,m}:=(x_1x_2\cdots x_m,\; x_2x_3\cdots x_{m+1},\; \ldots,\; x_{n-m+1}\cdots x_n, x_{n-m+2}\cdots x_nx_1, \ldots, x_nx_1\cdots x_{m-1})\) be the \(m\)-path ideal of the cycle graph of length \(n\), in the ring of polynomials \(S=K[x_1,\ldots,x_n]\).
As a continuation of a previous paper, we prove several new results regarding \(\depth(S/J_{n,m}^t)\) and \(\sdepth(S/J_{n,m}^t)), where \(t\geq 1\).
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