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), 33273336
MSC (2010):
Primary 13C15, 05E99; Secondary 13C13
Published electronically:
June 7, 2013
MathSciNet review:
3080155
Fulltext PDF
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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 111559415, Tehran, Iran – and – School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 193955746, Tehran, Iran
Email:
pournaki@ipm.ir
S. A. Seyed Fakhari
Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 111559415, 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 193955746, Tehran, Iran
Email:
yassemi@ipm.ir
DOI:
http://dx.doi.org/10.1090/S000299392013115947
PII:
S 00029939(2013)115947
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
