Krawtchouk多项式和Krawtchouk矩阵
Krawtchouk polynomials and Krawtchouk matrices
摘要：
Krawtchouk矩阵具有Krawtchouk多项式的值作为非负整数参数的条目。我们展示了它们是如何通过一个二进制洗牌函数作为凝聚西尔维斯特-阿达玛矩阵出现的。给出了基本的对称张量代数。我们的方法是用来解决Kac的制定的Escherifest瓮模型。连接与量子和经典的随机游动以及各种扩展的经典多项式。
英文摘要：
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 presented. Our approach is used to solve Kac' formulation of the Ehrenfest urn model. Connections with quantum and classical random walks are shown as well as various extensions of the classical polynomials.
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