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Fractional Jumps: Complete Characterisation and an Explicit Infinite Family

  • Federico Amadio Guidi
  • Giacomo Micheli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11321)

Abstract

In this paper we provide a complete characterisation of transitive fractional jumps. In particular, we prove that they can only arise from transitive projective automorphisms apart from a couple of degenerate cases which we entirely classify. 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.

Notes

Acknowledgment

The authors are grateful to Andrea Ferraguti for preliminary reading of this manuscript, and for useful discussions and suggestions. The second author is thankful to the Swiss National Science Foundation grant number 171248.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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