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Abstract
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Let I be a matroidal ideal of degree d of a polynomial ring R = K[x_1, ..., x_n], where K is a field. Let astab(I) and dstab(I) be the smallest integers m and n, for which Ass(I^m) and depth(I^n ) stabilize, respectively. In this paper, we show that astab(I) = 1 if and only if dstab(I) = 1. Moreover, we prove that if d = 3, then astab(I) = dstab(I). Furthermore, we show that if I is an almost square-free Veronese type ideal of degree d, then astab(I) = dstab(I) = ⌈ n−1/n−d ⌉
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