Fractional jumps: complete characterisation and an explicit infinite family

Federico Amadio Guidi; Giacomo Micheli

doi:10.1007/978-3-030-05153-2_14

paper

Fractional jumps: complete characterisation and an explicit infinite family

arXiv:1805.11658 · doi:10.1007/978-3-030-05153-2_14

Abstract

In this paper we provide a complete characterisation of transitive fractional jumps by showing that they can only arise from transitive projective automorphisms. Furthermore, we prove that such construction is feasible for arbitrarily large dimension by exhibiting an infinite class of projectively primitive polynomials whose companion matrix can be used to define a full orbit sequence over an affine space.