Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences

Details Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences

2000-10-18

arxiv.org/abs/math/0010186v1

Mathematics

Combinatorics

13 pages

Scientific paper

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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