Skip to main content
Log in

Multigraded shifts of matroidal ideals

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

In this paper, we show that if I is a matroidal ideal, then the ideal generated by the i-th multigraded shifts is also a matroidal ideal for every \(i=0,\ldots ,{\text {proj dim}}(I)\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Chiang-Hsieh, H.: Some arithmetic properties of matroidal ideals. Commun. Algebra 38(3), 944–952 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Conca, A., Herzog, J.: Castelnuovo–Mumford regularity of products of ideals. Collect. Math. 54, 137–152 (2003)

    MathSciNet  MATH  Google Scholar 

  3. Herzog, J., Hibi, T.: Monomial ideals. In: Graduate Texts in Mathematics, Vol. 260. Springer-Verlag London Ltd., London (2011)

  4. Herzog, J., Takayama, Y.: Resolutions by mapping cones. Homology Homotopy Appl. 4(2), 277–294 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Johnsen, T., Roksvold, J., Verdure, H.: Betti numbers associated to the facet ideal of a matroid. Bull. Braz. Math. Soc. N. Ser. 45(4), 727–744 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Maurer, S.B.: Matroid base graphs I. J. Comb. Theory B 14, 216–240 (1973)

    Article  MATH  Google Scholar 

  7. Mohammadi, F., Moradi, S.: Weakly polymatroidal ideals with applications to vertex cover ideals. Osaka J. Math. 47(3), 627–636 (2010)

    MathSciNet  MATH  Google Scholar 

  8. Novik, I., Postnikov, A., Sturmfels, B.: Syzygies of oriented matroids. Duke Math. J. 111(2), 287–317 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Oxley, J.G.: Matroid Theory. Oxford University Press, Oxford (2006)

    MATH  Google Scholar 

  10. Tchernev, A.B.: Representations of matroids and free resolutions for multigraded modules. Adv. Math. 208(1), 75–134 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shamila Bayati.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bayati, S. Multigraded shifts of matroidal ideals. Arch. Math. 111, 239–246 (2018). https://doi.org/10.1007/s00013-018-1216-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-018-1216-7

Mathematics Subject Classification

Keywords

Navigation