Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences

2000/10/18 by Rhodes Peele, Peele, Rhodes, Pantelimon Stănică +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Mathematics and Applications #math.CO #math.NT #msc:05A10 #msc:11B39 #msc:11B65 #msc:11C20 #msc:15A33 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0010186

13 pages

arxiv created 2000/10/18 · arxiv updated 2009/11/30

Abstract

If L, respectively R are matrices with entries binomi-1,j-1, respectively binomi-1,n-j, it is known that L² = I (mod 2), respectively R³ = 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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