Skip to main content
SpringerLink
Log in

Prisms and Pyramids of Shelling Components

  • Published:
Annals of Combinatorics Aims and scope Submit manuscript

Abstract

We study how the shelling components behave under the pyramid and prism operations. As a consequence we obtain a concise recursion for the cubical shelling contributions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bayer, M., Klapper, A.: A new index for polytopes. Discrete Comput. Geom. 6(1), 33–47 (1991)

    Article  MathSciNet  Google Scholar 

  2. du Plessis, A., Wall, T.: The Geometry of Topological Stability. London Mathematical Society Monographs. New Series, Vol. 9. The Clarendon Press, Oxford University Press, New York (1995)

  3. Ehrenborg, R., Goresky, M., Readdy, M.: Euler flag enumeration of Whitney stratified spaces. Adv. Math. 268, 85–128 (2015)

    Article  MathSciNet  Google Scholar 

  4. Ehrenborg, R., Hetyei, G.: Flags and shellings of Eulerian cubical posets. Ann. Combin. 4(2), 199–226 (2000)

    Article  MathSciNet  Google Scholar 

  5. Ehrenborg, R., Readdy, M.: Coproducts and the cd-index. J. Algebraic Combin. 8(3), 273–299 (1998)

    Article  MathSciNet  Google Scholar 

  6. Gibson, C.G., Wirthmüller, K., du Plessis, A., Looijenga, E.J.N.: Topological Stability of Smooth Mappings. Lecture Notes in Mathematics, Vol. 552. Springer-Verlag, Berlin-New York (1976)

  7. Goresky, M., MacPherson, R.: Stratified Morse Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], Vol. 14. Springer-Verlag, Berlin (1988)

  8. Hetyei, G.: On the \(cd\)-variation polynomials of André and Simsun permutations. Discrete Comput. Geom. 16(3), 259–276 (1996)

    Article  MathSciNet  Google Scholar 

  9. Mather, J.: Notes on Topological Stability. Harvard University, Cambridge (1970)

    MATH  Google Scholar 

  10. Stanley, R.P.: Flag \(f\)-vectors and the cd-index. Math. Z. 216(3), 483–499 (1994)

    Article  MathSciNet  Google Scholar 

  11. Stanley, R.P.: Enumerative Combinatorics, Vol. 1. Cambridge University Press, Cambridge (2012)

    MATH  Google Scholar 

Download references

Acknowledgements

The author thanks Margaret Readdy for her comments on an earlier draft of this paper. The author was partially supported by National Science Foundation grant DMS 0902063.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, KY, 40506, USA

    Richard Ehrenborg

Authors
  1. Richard Ehrenborg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Richard Ehrenborg.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ehrenborg, R. Prisms and Pyramids of Shelling Components. Ann. Comb. 22, 769–779 (2018). https://doi.org/10.1007/s00026-018-0412-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00026-018-0412-2

Mathematics Subject Classification

Keywords

Search

Navigation