Skip to main content
SpringerLink
Log in

Quasi-binomial coefficients stemming from Nakayama algebras

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

It is known that there is a very closed connection between the set of non-isomorphic indecomposable basic Nakayama algebras and the set of admissible sequences. To determine the cardinal number of all nonisomorphic indecomposable basic Nakayama algebras, we describe the cardinal number of the set of all t-length admissible sequences using a new type of integers called quasi-binomial coefficients. Furthermore, we find some intrinsic relations among binomial coefficients and quasi-binomial coefficients.

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. Assem I, Simson D, Skowronski A. Elements of the Representation Theory of Associative Algebras. Cambridge: Cambridge University Press, 2006

    Book  MATH  Google Scholar 

  2. Auslander M, Reiten I, Smal Mathematics, vol. 36. Cambridge: Cambridge University Press, 1994, 111–118

    Google Scholar 

  3. Fuller K R. Generalized uniserial rings and their Kupisch series. Math Z, 1968, 106: 248–260

    Article  MATH  MathSciNet  Google Scholar 

  4. Happel D, Seidel U. Piecewise hereditary Nakayama algebras. Algebr Rep Theory, 2010, 13: 693–704

    Article  MATH  MathSciNet  Google Scholar 

  5. Kupisch H. Beitrage zur Theorie nichthalbeinfacher Ringe mit Minimalbedingung. Crelles J, 1959, 201: 100–112

    MATH  MathSciNet  Google Scholar 

  6. Muchtadi-Alansyah I. Braid action on derived cateroy Nakayama algebras. Commun Algebras, 2008, 36: 2544–2569

    Article  Google Scholar 

  7. Nakayama T. Note on uniserial and generalized uniserial rings. Proc Imp Akad Japan, 1940, 16: 285–289

    Article  Google Scholar 

  8. Reiten I. The use of almost split sequences in the representation theory of Artin algebras. In: Lecture Notes in Mathematics, vol. 944. Berlin-New York: Springer-Verlag, 1982, 29–104

    Google Scholar 

  9. Skowronski A. Tame triangular matrix algebra over Nakayama algebra. J Lond Math Soc, 1986, 2: 245–264

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Information Science, Yantai University, Yantai, 264005, China

    RuChen Hou

  2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China

    GuangLian Zhang

Authors
  1. RuChen Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. GuangLian Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to RuChen Hou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hou, R., Zhang, G. Quasi-binomial coefficients stemming from Nakayama algebras. Sci. China Math. 57, 1545–1552 (2014). https://doi.org/10.1007/s11425-014-4780-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-014-4780-8

Keywords

MSC(2010)

Search

Navigation