2021/07/27 by Shalosh B. Ekhad, Doron Zeilberger, Ekhad, Shalosh B. +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2107.13092
openalex publication_date 2021/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A few years ago, Peter Larcombe discovered an amazing property regarding two by two matrices. For any such 2 by 2 matrix A, the ratios of the two anti-diagonal entries is the same for all powers of A. We discuss extensions to higher dimensions, and give a short bijective proof of Larcombe and Eric Fennessey's elegant extension to tri-diagonal matrices of arbitrary dimension. This article is accompanied by a Maple package.