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Valuations on Lattice Polytopes

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Tensor Valuations and Their Applications in Stochastic Geometry and Imaging

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2177))

Abstract

This survey is on classification results for valuations defined on lattice polytopes that intertwine the special linear group over the integers. The basic real valued valuations, the coefficients of the Ehrhart polynomial, are introduced and their characterization by Betke and Kneser is discussed. More recent results include classification theorems for vector and convex body valued valuations.

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Acknowledgements

The authors thank Raman Sanyal for pointing out Corollary 8.4 and its proof to them. They also thank Martin Henk for helpful remarks. The work of Károly J. Böröczky was supported, in part, by the Hungarian Scientific Research Fund No 109789 and No 116451, and the work of Monika Ludwig was supported, in part, by Austrian Science Fund (FWF) Project P25515-N25.

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Authors and Affiliations

  1. Department of Mathematics and Its Applications, Central European University, Nador u 9, 1051, Budapest, Hungary

    Károly J. Böröczky

  2. Rényi Institute, Realtanoda u 13–15, 1053, Budapest, Hungary

    Károly J. Böröczky

  3. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8–10, 1040, Vienna, Austria

    Monika Ludwig

Authors
  1. Károly J. Böröczky
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Correspondence to Monika Ludwig .

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Editors and Affiliations

  1. Department of Mathematics, Aarhus University, Aarhus C, Denmark

    Eva B. Vedel Jensen

  2. Department of Mathematics, Aarhus University, Aarhus C, Denmark

    Markus Kiderlen

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Böröczky, K.J., Ludwig, M. (2017). Valuations on Lattice Polytopes. In: Jensen, E., Kiderlen, M. (eds) Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Lecture Notes in Mathematics, vol 2177. Springer, Cham. https://doi.org/10.1007/978-3-319-51951-7_8

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