Corpus ID: 5329904

Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences

@article{Peele2000MatrixPO,
  title={Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences},
  author={R. Peele and P. Stănică},
  journal={arXiv: Combinatorics},
  year={2000}
}
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. 
6 Citations
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