Factorials & Binomial Coefficients in Polynomial Rings Over Finite Fields

  • William A. Kimball

Abstract

Carlitz [1], [2] has given a definition of a type of “binomial coefficient” for polynomial rings over finite fields. In this paper a different definition will be provided and some of its fundamental properties will be established.

Keywords

Finite Field Unpublished Manuscript Polynomial Ring Irreducible Polynomial Monic Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Carlitz, Leonard. “On Certain Functions Connected with Polynomials in a Galois Field”. Duke Mathematical Journal, Vol. 1.2 (1935) June.Google Scholar
  2. [2]
    Carlitz, Leonard. “An Analogue of the Von-Staudt Clausen Theorem”. Duke Mathematical Journal, Vol. 3.3 (1937) September.Google Scholar
  3. [3]
    Granville, Andrew. “Binomial coefficients Modulo Prime Powers”. Unpublished manuscript.Google Scholar
  4. [4]
    Granville, Andrew. “Binomial coefficients Modulo Prime Powers”. Unpublished manuscript.Google Scholar
  5. [5]
    Hardy and Wright. “An Introduction to the Theory of Numbers”. Oxford Sciences Publications. 1989, p. 63.Google Scholar
  6. [6]
    Ireland, Kenneth and Rosen, Michael. “A Classical Introduction to Modern Number Theory”. Springer-Verlag, 1992. p. 40.Google Scholar
  7. [7]
    Lang, Serge. “Algebra”. Addison-Wesley, Menlo Park, CA, 1984. p. 67.MATHGoogle Scholar
  8. [8]
    Long, Calvin T. “An Elementary Introduction to Number Theory”. Prentice Hall, Englewood Cliffs, NJ, 1987. p. 64.Google Scholar
  9. [9]
    McCarthy, Paul J. “Algebraic Extensions of Fields”. Dover, New York, 1976. p. 77.MATHGoogle Scholar
  10. [10]
    McCoy, Neal H. “Rings and Ideals”. The Mathematical Association of America, (1962): p. 40.Google Scholar
  11. [11]
    Singmaster, David. “Divisibility of Binomial and Multinomial Coefficients by Primes and Prime Powers”. From a Collection of Manuscripts Related to the Fibonacci Sequence.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • William A. Kimball

There are no affiliations available

Personalised recommendations