Depth and Stanley depth of the path ideal associated to an n-cyclic graph

2016/12/24 by Zhu, Guangjun
#13C15 #13F20 #13P10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.08177

Abstract

We compute the depth and Stanley depth for the quotient ring of the path ideal of length 3 associated to a n-cyclic graph, given some precise formulas for depth when n\not≡ 1 (mod 4), tight bounds when n≡ 1 (mod 4) and for Stanley depth when n≡ 0,3 (mod 4), tight bounds when n≡ 1,2 (mod 4). Also, we give some formulas for depth and Stanley depth of a quotient of the path ideals of length n-1 and n.

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