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arXiv math/00101862000-10-18math.COmath.NT

列对齐杨辉三角形和Fibonacci序列的矩阵幂

Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences

Rhodes Peele, Pantelimon Stanica

备注：: 13 pages

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摘要：

如果L和R分别是元素为binom{i-1，j-1}和binom{i-1，n-j}的矩阵，则已知L^2 = I（mod 2），R^3 = I（mod 2），其中I是n维> 1的单位矩阵（参见P10735- 1999年5月的《美国数学月刊》）。我们将它推广到任何素数p，并给出了一个美丽的连接到斐波那契数。

英文摘要：

If L, respectively R are matrices with entries binom{i-1,j-1}, respectively binom{i-1,n-j}, it is known that L^2 = I (mod 2), respectively R^3 = I (mod 2), where I is the identity matrix of dimension n > 1 (see P10735-May 1999 issue of the American Mathematical Monthly). We generalize it for any prime p, and give a beautiful connection to Fibonacci numbers.

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