Krawtchouk Polynomials and Krawtchouk Matrices

Philip Feinsilver and Jerzy Kocik ()
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Philip Feinsilver: Southern Illinois University, Department of Mathematics
Jerzy Kocik: Southern Illinois University, Department of Mathematics

A chapter in Recent Advances in Applied Probability, 2005, pp 115-141 from Springer

Abstract: 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.

Keywords: Krawtchouk polynomials; Hadamard matrices; symmetric tensors; Krawtchouk encyclopedia (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-23394-9_5

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DOI: 10.1007/0-387-23394-6_5

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