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Dimension Quasi-polynomials of Inversive Difference Field Extensions with Weighted Translations

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Mathematical Aspects of Computer and Information Sciences (MACIS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10693))

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Abstract

We consider Hilbert-type functions associated with finitely generated inversive difference field extensions and systems of algebraic difference equations in the case when the translations are assigned positive integer weights. We prove that such functions are quasi-polynomials that can be represented as alternating sums of Ehrhart quasi-polynomials of rational conic polytopes. In particular, we generalize the author’s results on difference dimension polynomials and their invariants to the case of inversive difference fields with weighted basic automorphisms.

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Authors and Affiliations

  1. The Catholic University of America, Washington, DC, 20064, USA

    Alexander Levin

Authors
  1. Alexander Levin
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Correspondence to Alexander Levin .

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Editors and Affiliations

  1. University of Paderborn, Paderborn, Germany

    Johannes Blömer

  2. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  3. Johannes Kepler University Linz, Linz, Austria

    Temur Kutsia

  4. SBA Research, Vienna, Austria

    Dimitris E. Simos

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Levin, A. (2017). Dimension Quasi-polynomials of Inversive Difference Field Extensions with Weighted Translations. In: Blömer, J., Kotsireas, I., Kutsia, T., Simos, D. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2017. Lecture Notes in Computer Science(), vol 10693. Springer, Cham. https://doi.org/10.1007/978-3-319-72453-9_5

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  • DOI: https://doi.org/10.1007/978-3-319-72453-9_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72452-2

  • Online ISBN: 978-3-319-72453-9

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