Skip to main content
SpringerLink
Log in

The bijection between plane partitions and nonnegative integer matrices

  • Published:
Lithuanian Mathematical Journal Aims and scope Submit manuscript

Abstract

The one-to-one correspondence between the set of plane partitions withr rows andm columns and the set of matrices of nonnegative integers with the same numbers of rows and columns has been constructed.

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. G. E. Andrews,The Theory of Partitions, Addison-Wesley (1976).

  2. P. A. MacMahon,Combinatory Analysis, Cambridge Univ. Press (1916); reprinted by Chelsea (1960).

  3. D. E. Knuth and E. A. Bender, Enumeration of plane partitions,J. Comb. Theory,A13, 40–54 (1972).

    MathSciNet  Google Scholar 

  4. R. P. Stanley, The conjugate trace of a plane partition,J. Comb. Theory,A14, 53–65 (1973).

    MATH  MathSciNet  Google Scholar 

  5. R. P. Stanley, Theory and application of plane partitions,Stud. Appl. Math.,50, 167–188, 259–279 (1971).

    MATH  MathSciNet  Google Scholar 

  6. D. E. Knuth, Permutations, matrices, and generalized Young tableaux,Pacific J. Math. 34, 709–727 (1970).

    MATH  MathSciNet  Google Scholar 

  7. W. H. Burge, Four correspondences between graphs and generalized Young tableaux,J. Comb. Theory,A27, 12–30 (1974).

    MathSciNet  Google Scholar 

  8. A. A. Jucys, Tournaments and generalized Young tableaux,Mat. Zametki,27, 353–359 (1980).

    MathSciNet  Google Scholar 

  9. C. Schensted, Longest increasing and decreasing subsequence,Can. J. Math.,13, 179–191 (1961).

    MATH  MathSciNet  Google Scholar 

  10. A. A. Jucys, Generalization of the enumeration problem of partitions. Multiplicities of the symmetric group representations,Liet. Fiz. Rinkinys,26, 513–528 (1986).

    MathSciNet  Google Scholar 

  11. A. O. Barut and r. Rączka,Theory of Group Representations and Applications, PWN — Polish Scientific Publishers (1977).

  12. A. A. Jucys, Representations of the symmetric groups and the Clebsch-Gordon coefficients of the unitary groups,Lith. Math. J.,8, 597–609 (1968).

    MathSciNet  Google Scholar 

Download references

Authors
  1. A. A. Jucys
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Institute of Theoretical Physics and Astronomy, Goštauto 12, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 2, pp. 204–210, April–June, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jucys, A.A. The bijection between plane partitions and nonnegative integer matrices. Lith Math J 35, 163–167 (1995). https://doi.org/10.1007/BF02341495

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02341495

Keywords

Search

Navigation