Krawtchouk Polynomials and Krawtchouk Matrices [chapter]

Philip Feinsilver, Jerzy Kocik
Recent Advances in Applied Probability  
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
more » ... in the concluding section. Interested folks are encouraged to visit the website http://chanoir.math.siu.edu/wiki/KravchukEncyclopedia which is currently in a state of development. What are Krawtchouk matrices Of Sylvester-Hadamard matrices and Krawtchouk matrices, the latter are less familiar, hence we start with them.
doi:10.1007/0-387-23394-6_5 fatcat:m7ztpc2f6fbhlaex4rexxovqx4