INTEGRAL POLYNOMIAL SEQUENCES RELATED WITH KRAWTCHOUK MATRICES AND ASSOCIATED RIORDAN ARRAYS Ju, Hyeong-Kwan; Lee, Hyun-Jeong; Seo, Soo-Jeong;
The relationship between the integral polynomials obtained from the iterations of the matrix given by the expression (1) and the entries of the Krawtchouk matrices is derived by using the associated Riordan arrays.
Sergey V. Avgustinovich, On a property of perfect binary codes, (Russian)Diskret.Anal.Issled.Oper. vol.2(1995), no.1, 4-6.
Paul Barry, A note on Krawtchouk polynomials and Riordan arrays, J. of Integer Sequences, vol.11(2008) Article 08.2.2, 1-16.
Gi-Sang Cheon and Yongdo Lim, Integral polynomial sequences arising from the matrix powers of order 2, to appear in Linear Algebra and Its Applications.
Phillip Feinsilver and Jerzy Kocik, Krawtchouk polynomials and Krawtchouk matrices, Recent Advances in Applied Probability, Spring-Verlag, October, 2004. See also http://aps.arxiv.org/abs/quant-ph/0702073.
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Jong Yoon Hyun, Private communication.
Yongdo Lim, Integral polynomial sequences from weighted Delannoy numbers, materials presented at Chonnam National University on August 2010.
On-Line Encyclopedia of Integer Sequences, available at http://oeis.org/