Abstract
Abstract: Let S = K[x1, . . . , xn] be a polynomial ring over a field K in n variables and I a squarefree monomial ideal of S with Schmitt–Vogel number sv(I) . In this paper, we show that sdepth (I) ≥ max {1, n− 1− ⌊ sv(I) 2 ⌋}, which improves the lower bound obtained by Herzog, Vladoiu, and Zheng. As some applications, we show that Stanley’s conjecture holds for the edge ideals of some special n -cyclic graphs with a common edge.
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