Skip to main content

Summary

q-Analogs of the Catalan number identities of Touchard, Jonah, and Koshy are derived.

Mathematics Subject Classification (2000) 05A10, 05A16, 05A30

Partially supported by National Science Foundation Grant DMS-0801184.

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

Access this chapter

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. G. E. Andrews, Applications of basic hypergeometric functions, SIAM Rev., 16 (1974), 441–484

    Article  MathSciNet  MATH  Google Scholar 

  2. G. E. Andrews, The theory of partitions. Encyclopedia of Mathematics and Its Applications, Vol. 2. (G. C. Rota, ed.) Addison-Wesley, Reading, MA, 1976 (Reprinted: Cambridge University Press, Cambridge, 1998)

    Google Scholar 

  3. G. E. Andrews, Catalan numbers, q-Catalan numbers and hypergeometric series, J. Combin. Theory A, 44 (1987), 267–273

    Article  MATH  Google Scholar 

  4. G. E. Andrews, On the difference of successive Gaussian polynomials, J. Stat. Plan. Inf., 34 (1993), 19–22

    Article  MATH  Google Scholar 

  5. W. N. Bailey, Generalized Hypergeometric Series. Cambridge Tracts in Mathematics and Mathematical Physics No. 32, Cambridge University Press, Cambridge, 1935 (Reprinted: Hafner, New York, 1964)

    MATH  Google Scholar 

  6. J. Fürlinger and J. Hofbauer, q-Catalan numbers, J. Combin. Theory A, 40 (1985), 248–264

    Article  MATH  Google Scholar 

  7. G. Gasper and M. Rahman, Basic Hypergeometric Series. Encyclopedia of Mathematics and Its Applications, Vol. 35, Cambridge University Press, Cambridge, 1990

    MATH  Google Scholar 

  8. H. W. Gould, Bell and Catalan Numbers: Research Bibliography of Two Special Number Sequences, rev. ed., Combinatorial Research Institute, Morgantown, WV, 1978

    Google Scholar 

  9. P. Hilton and J. Pedersen, The ballot problem and Catalan numbers, Nieuw Arch. Wisk., 7–8 (1990), 209–216

    MathSciNet  Google Scholar 

  10. T. Koshy, Catalan Numbers with Applications, Oxford University Press, New York, 2009

    MATH  Google Scholar 

  11. R. P. Stanley, Enumerative Combinatorics, Vol. 1, Wadsworth & Brooks/Cole, Monterey, CA, 1986

    MATH  Google Scholar 

  12. R. P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge University Press, New York, 1999

    Book  Google Scholar 

  13. R. P. Stanley, Catalan Addendum, http://www-math.mit.edu/~rstan/ec/catadd.pdf, version 6, October 2008

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to George E. Andrews .

Editor information

Editors and Affiliations

Additional information

Dedicated to the memory of Professor Alladi Ramakrishnan

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer New York

About this chapter

Cite this chapter

Andrews, G.E. (2010). q-Catalan Identities. In: Alladi, K., Klauder, J., Rao, C. (eds) The Legacy of Alladi Ramakrishnan in the Mathematical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6263-8_10

Download citation

Publish with us

Policies and ethics