Depth and Stanley depth of the facet ideals of some classes of simplicial complexes |
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Authors: | Xiaoqi Wei Yan Gu |
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Institution: | 1.School of Mathematical Sciences,Soochow University,Suzhou, Jiangsu,P.R. China |
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Abstract: | Let Δ n,d (resp. Δ′ n,d ) be the simplicial complex and the facet ideal I n,d = (x 1... x d, x d?k+1... x 2d?k ,..., x n?d+1... x n ) (resp. J n,d = (x 1... x d , x d?k+1... x 2d?k ,..., x n?2d+2k+1... x n?d+2k , x n?d+k+1... x n x 1... x k)). When d ≥ 2k + 1, we give the exact formulas to compute the depth and Stanley depth of quotient rings S/J n,d and S/I n,d t for all t ≥ 1. When d = 2k, we compute the depth and Stanley depth of quotient rings S/Jn,d and S/I n,d , and give lower bounds for the depth and Stanley depth of quotient rings S/I n,d t for all t ≥ 1. |
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