Skip to main content

Partitions and Generating Functions

  • Chapter
  • First Online:
Lessons in Enumerative Combinatorics

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 290))

  • 2408 Accesses

Abstract

Here we shall be concerned with manipulating objects built up from rows of squares as in Figure 2.1.

Rows of squares.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 69.99
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. Andrews, G.E.: The Theory of Partitions Chapter 7. Encyclopedia of Mathematics and Its Applications. Addison-Wesley, London (1976)

    Google Scholar 

  2. Euler, L.: Evolutio producti infiniti (1 − x)(1 − xx)(1 − x 3)(1 − x 4)(1 − x 5)(1 − x 6) etc. Acta Acad. Sci. Imperialis Petropolitanae 4, 47–55 (1783). Opera Omnia: Series 1 3, 472–479

    Google Scholar 

  3. Franklin, F.: Sur le développement du produit infini (1 − x)(1 − x 2)(1 − x 3)⋯. C. R. 82, 448–450 (1881)

    Google Scholar 

  4. Garsia, A.M., Milne, S. C.: A Rogers-Ramanujan bijection. J. Combin. Theory Ser. A 31, 289–339 (1981)

    Article  MathSciNet  Google Scholar 

  5. MacMahon, P.A.: Combinatory Analysis. Cambridge Univ. Press, London (1916); reprinted by Chelsea, NY, 1960

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Eğecioğlu, Ö., Garsia, A.M. (2021). Partitions and Generating Functions. In: Lessons in Enumerative Combinatorics. Graduate Texts in Mathematics, vol 290. Springer, Cham. https://doi.org/10.1007/978-3-030-71250-1_2

Download citation

Publish with us

Policies and ethics