2021/03/23 by Shalosh B. Ekhad, Doron Zeilberger, Ekhad, Shalosh B. +1
Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.2103.12852
2 pages; Exclusively published in the Personal Journal of Shalosh B. Ekhad and this arxiv. Accompanied by a Maple package and output files available from https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/bijstern.html
arxiv created 2021/03/23 · openalex publication_date 2021/03/23 · arxiv updated 2021/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a delightful article, Richard Stanley derived, algebraically, the surprisingly simple formula, 3 times 7 to the power n-1, for the sum of the cubes of the n-th row of Stern's diatomic array. In this note, we find an elegant bijective proof of this surprising fact, that explains it and gives insight. The novelty is that this gorgeous bijection was discovered by a computer (SBE), with minimal guidance by a human (DZ). This debunks the conventional wisdom, held by some human supremacists, that computers can only compute, but they can't give insight