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Krawtchouk polynomials and Krawtchouk matrices. (English) Zbl 1075.33003

Baeza-Yates, Ricardo (ed.) et al., Recent advances in applied probability. Papers presented at the international workshop on applied probability, IWAP 2002, Caracas, Venezuela, January 14–17, 2002. New York, NY: Springer (ISBN 0-387-23378-4/hbk). 115-141 (2005).
The authors study Krawtchouk matrices whose entries consist of the values of Krawtchouk polynomials of a given order. They show that these matrices arise in various places of mathematics. In particular a connection to Sylvester-Hadamard matrices, Ehrenfest urn model and Bernouli random walk is discussed. The paper ends with the list of topics in the Krawtchouk Encyclopedia, an authors’ project, still in development.
For the entire collection see [Zbl 1057.60002].

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
15A69 Multilinear algebra, tensor calculus
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A triangle of Krawtchouk coefficients.