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Stanley depth of powers of the edge ideal of a forest

Pournaki, M. R ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1090/S0002-9939-2013-11594-7
  3. Publisher: 2013
  4. Abstract:
  5. Let K be a field and S = K[x1,...,xn] be the polynomial ring in n variables over the field K. 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 I 1 ≤ i ≤ p}. Morey has shown that for every t ≥ 1, the quantity max 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
  6. Keywords:
  7. Edge ideal ; Monomial ideal ; Stanley conjecture ; Stanley depth
  8. Source: Proceedings of the American Mathematical Society ; Volume 141, Issue 10 , 2013 , Pages 3327-3336 ; 00029939 (ISSN)
  9. URL: http://www.ams.org/journals/proc/2013-141-10/S0002-9939-2013-11594-7/home.html