A lower bound for depths of powers of edge ideals

作者：Fouli Louiza^*; Morey Susan

来源：Journal of Algebraic Combinatorics, 2015, 42(3): 829-848.

DOI：10.1007/s10801-015-0604-3

• Edge ideal
• Depth
• Powers of ideals
• Stanley depth
• Projective dimension
• Monomial ideal

Let be a graph, and let be the edge ideal of . Our main results in this article provide lower bounds for the depth of the first three powers of in terms of the diameter of . More precisely, we show that , where is the diameter of and is the number of connected components of and . For general powers of edge ideals we show that . As an application of our results we obtain the corresponding lower bounds for the Stanley depth of the first three powers of .

• 出版日期2015-11