Skip to main content
SpringerLink
Log in

Chain Blockers and Convoluted Catalan Numbers

  • Published:
Order Aims and scope Submit manuscript

Abstract

We give new interpretations of Catalan and convoluted Catalan numbers in terms of trees and chain blockers. For a poset P we say that a subset A ⊆ P is a chain blocker if it is an inclusionwise minimal subset of P that contains at least one element from every maximal chain. In particular, we study the set of chain blockers for the class of posets P = C a × C b where C i is the chain 1 < ⋯ < i. We show that subclasses of these chain blockers are counted by Catalan and convoluted Catalan numbers.

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. Catalan, E.: Sur les nombres de Segner. Rend. Circ. Mat. Palermo 1, 190–201 (1887)

    Article  MATH  Google Scholar 

  2. Foldes, S., Woodroofe, R.: Antichain cutsets of strongly connected posets. Order 30, 351–361 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Regev, A.: A proof of Catalan’s convolution formula. Integers 12, #A29 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Rival, I., Zaguia, N.: Antichain cutsets. Order 1, 235247 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  5. Stanley, R.P.: Catalan Numbers. Cambridge University Press, Cambridge (2015)

    Book  MATH  Google Scholar 

  6. Tedfordm, S.J.: Combinatorial interpretations of convolutions of the Catalan numbers. Integers 11, #A3 (2011)

    MathSciNet  MATH  Google Scholar 

  7. West, J.: Generating trees and the Catalan and Schröder numbers. Discret. Math. 146, 247–262 (1995)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. COMSATS Institute of Information Technology, Lahore, Pakistan

    Sarfraz Ahmad

  2. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, 35032, Marburg, Germany

    Volkmar Welker

Authors
  1. Sarfraz Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Volkmar Welker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sarfraz Ahmad.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahmad, S., Welker, V. Chain Blockers and Convoluted Catalan Numbers. Order 33, 347–358 (2016). https://doi.org/10.1007/s11083-015-9370-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11083-015-9370-z

Keywords

Search

Navigation