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Stanley depth of weakly 0-decomposable ideals

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Abstract

Recently, Seyed Fakhari proved that if I is a weakly polymatroidal monomial ideal in \({S\,=\,\mathbb{K}[x_1,\ldots,x_n]}\), then Stanley’s conjecture holds for S/I, namely, sdepth \({(S/I)\,\geq\, {\rm depth}(S/I)}\). We generalize his ideas and introduce several new classes of monomial ideals which also share this property. In particular, if I is the Stanley–Reisner ideal of the Alexander dual of a nonpure vertex decomposable simplicial complex, then Stanley’s conjecture holds for S/I.

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References

  1. Cimpoeaş M.: Several inequalities regarding Stanley depth. Rom. J. Math. Comput. Sci. 2, 28–40 (2012)

    MATH  MathSciNet  Google Scholar 

  2. Herzog J., Vladoiu M., Zheng X.: How to compute the Stanley depth of a monomial ideal. J. Algebra 322, 3151–3169 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Moradi and F. Khosh-Ahang, On vertex decomposable simplicial complexes and their Alexander duals (2013), arxiv:1302.594.

  4. Nagel U., Römer T.: Glicci simplicial complexes. J. Pure Appl. Algebra 212, 2250–2258 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Okazaki R., Yanagawa K.: Alexander duality and Stanley depth of multigraded modules. J. Algebra. 340, 35–52 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Rahmati Asghar and S. Yassemi, k-decomposable monomial ideals, Algebra Colloq., to appear.

  7. Rauf A.: Depth and Stanley depth of multigraded modules. Comm. Algebra 38, 773–784 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Seyed Fakhari S.A.: Stanley depth of weakly polymatroidal ideals. Archiv der Mathematik 103, 229–233 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  9. Sharifan L., Varbaro M.: Graded Betti numbers of ideals with linear quotients. Matematiche (Catania). 63, 257–265 (2008)

    MATH  MathSciNet  Google Scholar 

  10. Y.-H. Shen, Monomial ideals with linear quotients and componentwise (support-) linearity (2014), arxiv:1404.216.

  11. Stanley R. P.: Linear Diophantine equations and local cohomology. Invent Math. 68, 175–193 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  12. Yanagawa K.: Sliding functor and polarization functor for multigraded modules. Comm. Algebra. 40, 1151–1166 (2012)

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Wu Wen-Tsun Key Laboratory of Mathematics of CAS, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China

    Yi-Huang Shen

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  1. Yi-Huang Shen
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Correspondence to Yi-Huang Shen.

Additional information

This work was supported by the National Natural Science Foundation of China (#11201445) and the Fundamental Research Funds for the Central Universities.

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Shen, YH. Stanley depth of weakly 0-decomposable ideals. Arch. Math. 104, 3–9 (2015). https://doi.org/10.1007/s00013-014-0718-1

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  • DOI: https://doi.org/10.1007/s00013-014-0718-1

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