Linear divisibility sequences and Salem numbers
Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru
TL;DR
This paper characterizes order 4 linear divisibility sequences through their polynomials, shows their factorization into order 2 sequences, and uncovers a novel link with Salem numbers via modular generation.
Contribution
It introduces a new characterization and factorization method for order 4 sequences and establishes a novel connection with Salem numbers.
Findings
Order 4 sequences characterized by their polynomials
Sequences factor into order 2 divisibility sequences
Salem numbers generate order 4 sequences modulo 1
Abstract
We study linear divisibility sequences of order 4, providing a characterization by means of their characteristic polynomials and finding their factorization as a product of linear divisibility sequences of order 2. Moreover, we show a new interesting connection between linear divisibility sequences and Salem numbers. Specifically, we generate linear divisibility sequences of order 4 by means of Salem numbers modulo 1.
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Taxonomy
TopicsCoding theory and cryptography · semigroups and automata theory · Finite Group Theory Research