The Algebraic Theory of Fractional Jumps

TL;DR

This paper advances the algebraic understanding of fractional jumps by providing new constructions, extending generator methods, and offering fresh insights into their properties and primitive polynomials.

Contribution

It introduces an efficient construction method for fractional jumps, extends generator techniques, and presents new theoretical results on their properties.

Findings

Efficient construction of fractional jumps from projective maps

Extension of generator methods to fractional jump sequences

New results on absolute jump index and projectively primitive polynomials

Abstract

In this paper we start by briefly surveying the theory of Fractional Jumps and transitive projective maps. Then, we give an efficient construction of a fractional jump of a projective map and we extend the compound generator construction for the Inversive Congruential Generator to Fractional jump sequences. In addition, we provide new results on the absolute jump index, on projectively primitive polynomials, and on the explicit description of fractional jump generators.