Depth and Stanley depth of the facet ideals of some classes of simplicial complexes

作者：Wei, Xiaoqi; Gu, Yan^*

来源：Czechoslovak Mathematical Journal, 2017, 67(3): 753-766.

DOI：10.21136/CMJ.2017.0172-16

• monomial ideal
• facet ideal
• depth
• Stanley depth

Let Delta (n,d) (resp. Delta' (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 nd Stnley depth of quotient rings S/Jn,d nd S/I (n,d) , nd give lower bounds for the depth nd Stnley depth of quotient rings S/I (n,d) (t) for ll t >= 1.

• 出版日期2017-9
• 单位苏州大学