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29 March 2024
 
  » arxiv » math.CO/0010186

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Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences
Rhodes Peele ; Pantelimon Stanica ;
Date 19 Oct 2000
Subject Combinatorics; Number Theory MSC-class: 05A10; 11B39; 11B65; 11C20; 15A33 | math.CO math.NT
AbstractIf 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.
Source arXiv, math.CO/0010186
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