Skip to main content
SpringerLink
Log in

A Good Leaf Order on Simplicial Trees

  • Conference paper
  • First Online:
Connections Between Algebra, Combinatorics, and Geometry

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 76))

Abstract

Using the existence of a good leaf in every simplicial tree, we order the facets of a simplicial tree in order to find combinatorial information about the Betti numbers of its facet ideal. Applications include an Eliahou–Kervaire splitting of the ideal, as well as a refinement of a recursive formula of Hà and Van Tuyl for computing the graded Betti numbers of simplicial trees.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Caboara, M., Faridi, S., Selinger, P.: Simplicial cycles and the computation of simplicial trees. J. Symb. Comput. 42(1–2), 74–88 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Eliahou, S., Kervaire, M.: Minimal resolutions of some monomial ideals. J. Algebra 129(1), 1–25 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  3. Faridi, S.: The facet ideal of a simplicial complex. Manuscripta Math. 109, 159–174 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Faridi, S.: Cohen-Macaulay properties of square-free monomial ideals. J. Comb. Theory Ser. A 109(2), 299–329 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fatabbi, G.: On the resolution of ideals of fat points. J. Algebra 242(1), 92–108 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Fröberg, R.: A study of graded extremal rings and of monomial rings. Math. Scand. 51, 22–34 (1982)

    MATH  MathSciNet  Google Scholar 

  7. Gasharov, V., Peeva, I., Welker, V.: The lcm-lattice in monomial resolutions. Math. Res. Lett. 6(5–6), 521–532 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Grayson, D.R., Stillman, M.E.: Macaulay2, a software system for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2/Citing/

  9. Hà, H.T., Van Tuyl, A.: Splittable ideals and the resolutions of monomial ideals. J. Algebra 309, 405–425 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Herzog, J., Hibi, T., Trung, N.V., Zheng, X.: Standard graded vertex cover algebras, cycles and leaves. Trans. Am. Math. Soc. 360(12), 6231–6249 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Villarreal, R.: Monomial Algebras. Monographs and Textbooks in Pure and Applied Mathematics, vol. 238. Dekker, New York (2001)

    Google Scholar 

  12. Zheng, X.: Homological properties of monomial ideals associated to quasi-trees and lattices. Ph.D. thesis, Universität Duisburg-Essen (August 2004)

    Google Scholar 

Download references

Acknowledgments

The author acknowledges the financial support of NSERC and the hospitality of MSRI in Berkeley, CA where part of this work was completed.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Dalhousie University, 6316 Coburg Rd, 15000, Halifax, NS, Canada, B3H 4R2

    Sara Faridi

Authors
  1. Sara Faridi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sara Faridi .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan, USA

    Susan M. Cooper

  2. Department of Mathematics, North Dakota State University, Fargo, North Dakota, USA

    Sean Sather-Wagstaff

Additional information

Dedicated to Tony Geramita for his many contributions to Mathematics

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this paper

Cite this paper

Faridi, S. (2014). A Good Leaf Order on Simplicial Trees. In: Cooper, S., Sather-Wagstaff, S. (eds) Connections Between Algebra, Combinatorics, and Geometry. Springer Proceedings in Mathematics & Statistics, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0626-0_4

Download citation

Publish with us

Policies and ethics

Search

Navigation