Stanley depth of powers of the edge ideal of a forest

Authors:
M. R. Pournaki, S. A. Seyed Fakhari and S. Yassemi

Journal:
Proc. Amer. Math. Soc. **141** (2013), 3327-3336

MSC (2010):
Primary 13C15, 05E99; Secondary 13C13

DOI:
https://doi.org/10.1090/S0002-9939-2013-11594-7

Published electronically:
June 7, 2013

MathSciNet review:
3080155

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a field and be the polynomial ring in variables over the field . Let be a forest with connected components and let be its edge ideal in . Suppose that is the diameter of , , and consider . Morey has shown that for every , the quantity is a lower bound for . In this paper, we show that for every , the mentioned quantity is also a lower bound for . 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.

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Additional Information

**M. R. Pournaki**

Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11155-9415, Tehran, Iran – and – School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

Email:
pournaki@ipm.ir

**S. A. Seyed Fakhari**

Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11155-9415, Tehran, Iran

Email:
fakhari@ipm.ir

**S. Yassemi**

Affiliation:
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran – and – School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

Email:
yassemi@ipm.ir

DOI:
https://doi.org/10.1090/S0002-9939-2013-11594-7

Keywords:
Edge ideal,
monomial ideal,
Stanley depth,
Stanley conjecture

Received by editor(s):
August 25, 2011

Received by editor(s) in revised form:
December 10, 2011

Published electronically:
June 7, 2013

Additional Notes:
The research of the first and third authors was partially supported by grants from IPM (No. 90130073 and No. 90130214)

Communicated by:
Irena Peeva

Article copyright:
© Copyright 2013
American Mathematical Society