Geodesic
NONINCREASING DEPTH FUNCTIONS OF MONOMIAL IDEALS
Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 505-511

Voir la notice de l'article provenant de la source Cambridge University Press

Given a nonincreasing function f : Z≥ 0 \{0} → Z≥ 0 such that (i) f(k) − f(k + 1) ≤ 1 for all k ≥ 1 and (ii) if a = f(1) and b = limk → ∞f(k), then |f−1(a)| ≤ |f−1(a − 1)| ≤ ··· ≤ |f−1(b + 1)|, a system of generators of a monomial ideal I ⊂ K[x1, . . ., xn] for which depth S/Ik = f(k) for all k ≥ 1 is explicitly described. Furthermore, we give a characterization of triplets of integers (n, d, r) with n > 0, d ≥ 0 and r > 0 with the properties that there exists a monomial ideal I ⊂ S = K[x1, . . ., xn] for which limk→∞ depth S/Ik = d and dstab(I) = r, where dstab(I) is the smallest integer k0 ≥ 1 with depth S/Ik0 = depth S/Ik0+1 = depth S/Ik0+2 = ···. 
MATSUDA, KAZUNORI; SUZUKI, TAO; TSUCHIYA, AKIYOSHI. NONINCREASING DEPTH FUNCTIONS OF MONOMIAL IDEALS. Glasgow mathematical journal, Tome 60 (2018) no. 2, pp. 505-511. doi: 10.1017/S0017089517000349
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