2020/05/08 by Paul Barry, Barry, Paul
Mathematics · #11B83 #11C20 #11Y55 #11Y55 11B50 #15B36 #15B36 11B50 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Primary 11B50 #Secondary 05A15
paper · pdf · doi:10.48550/arxiv.2005.04066
openalex publication_date 2020/05/08 · openalex created_date 2020/05/13 · openalex updated_date 2026/07/28
Starting with a definition based on the Catalan numbers, we carry out an empirical study of the Rueppel sequence. We use the Hankel transform as the main technique. By means of this transform we find links to such sequences as the Jacobi sequence and the paper-folding sequence. We also study several number arrays defined by this sequence, which are analogs of the important Catalan triangles of combinatorics. We identify a sequence related to the Golay-Rudin-Shapiro sequence that plays a fundamental role in linking the Hankel transforms of the paper with classical sequences. Examples are given where certain privileged permutations appearing in the Leibnitz formula for determinants have a special role.