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Krawtchouk Polynomials and Krawtchouk Matrices

In: Recent Advances in Applied Probability

Author

Listed:
  • Philip Feinsilver

    (Southern Illinois University, Department of Mathematics)

  • Jerzy Kocik

    (Southern Illinois University, Department of Mathematics)

Abstract

Krawtchouk matrices have as entries values of the Krawtchouk polynomials for nonnegative integer arguments. We show how they arise as condensed Sylvester-Hadamard matrices via a binary shuffling function. The underlying symmetric tensor algebra is then presented. To advertise the breadth and depth of the field of Krawtchouk polynomials / matrices through connections with various parts of mathematics, some topics that are being developed into a Krawtchouk Encyclopedia are listed in the concluding section. Interested folks are encouraged to visit the website http://chanoir.math.siu.edu/Kravchuk/index.html which is currently in a state of development.

Suggested Citation

  • Philip Feinsilver & Jerzy Kocik, 2005. "Krawtchouk Polynomials and Krawtchouk Matrices," Springer Books, in: Ricardo Baeza-Yates & Joseph Glaz & Henryk Gzyl & Jürgen Hüsler & José Luis Palacios (ed.), Recent Advances in Applied Probability, pages 115-141, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-23394-9_5
    DOI: 10.1007/0-387-23394-6_5
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