“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 12193 |
|
||||
| Abstract: | |||||
|
Let \mathbbK be a field and S=\mathbbK[x1,...,xn] be the
polynomial ring in n variables over the field \mathbbK. Let G be a
forest with p connected components G1,…,Gp and let I=I(G) be its
edge ideal in S. Suppose that di is the diameter of Gi, 1 ≤ i ≤ p, and consider d = max{di | 1 ≤ i ≤ p}.
Morey has shown that for every t ≥ 1, the quantity max{⎡[(d−t+2)/3]⎤+p−1,p} is a lower bound for depth(S/It). In this paper, we show that for every t ≥ 1, the
mentioned quantity is also a lower bound for sdepth(S/It). By
combining this inequality with Burch's inequality, we show that any
sufficiently large powers of edge ideals of forests are Stanley. Finally,
we state and prove a generalization of our main theorem.
Download TeX format |
|||||
| back to top | |||||
