Skip to main content
SpringerLink
Log in

Enumeration of diagonally colored Young diagrams

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

In this note we give a new proof of a closed formula for the multivariable generating series of diagonally colored Young diagrams. This series also describes the Euler characteristics of certain Nakajima quiver varieties. Our proof is a direct combinatorial argument, based on Andrews’ work on generalized Frobenius partitions. We also obtain representations of these series in some particular cases as infinite products.

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. Fujii, Sh., Minabe, S.: A combinatorial study on quiver varieties. arXiv preprint (2005). arXiv:math/0510455

  2. Andrews, G.E.: Generalized Frobenius Partitions. Memoirs of the American Mathematical Society, vol. 301. AMS, Providence (1984)

  3. Fulton, W.: Young Tableaux: With Applications to Representation Theory and Geometry. London Mathematical Society Student Texts, vol. 35. Cambridge University Press, Cambridge (1997)

  4. Macdonald, I.G.: Symmetric Functions and Hall Polynomials. Oxford University Press, Oxford (1998)

    MATH  Google Scholar 

  5. Nakajima, H.: Geometric construction of representations of affine algebras. In: Proceedings of the International Congress of Mathematicians (Beijing, 2002), vol. I, IMU, Higher Ed, pp. 423–438 (2002)

  6. Sam, S.V., Tingley, P.: Combinatorial realizations of crystals via torus actions on quiver varieties. J. Algebraic Comb. 39(2), 271–300 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. James, G., Kerber, A.: The Representation Theory of the Symmetric Group. Encyclopedia of Mathematics and its Applications, vol. 16. Addison-Wesley Publishing Co., Reading (1981)

Download references

Acknowledgments

The author thanks to Balázs Szendrői, András Némethi and to the anonymous referee for numerous comments on earlier versions of this manuscript. The author was partially supported by the Lendület program of the Hungarian Academy of Sciences and by the ERC Advanced Grant LDTBud (awarded to András Stipsicz).

Author information

Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda utca 13-15, Budapest, 1053, Hungary

    Ádám Gyenge

Authors
  1. Ádám Gyenge
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ádám Gyenge.

Additional information

Communicated by A. Constantin.

This work was completed with the support of our TeX-pert.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gyenge, Á. Enumeration of diagonally colored Young diagrams. Monatsh Math 183, 143–157 (2017). https://doi.org/10.1007/s00605-016-0957-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00605-016-0957-2

Keywords

Mathematics Subject Classification

Search

Navigation