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A Product Formula for the Normalized Volume of Free Sums of Lattice Polytopes

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Advances in Algebra (SRAC 2017)

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Abstract

The free sum is a basic geometric operation among convex polytopes. This note focuses on the relationship between the normalized volume of the free sum and that of the summands. In particular, we show that the normalized volume of the free sum of full-dimensional polytopes is precisely the product of the normalized volumes of the summands.

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Notes

  1. 1.

    An alternative definition for mixed volume is the coefficient of \(\lambda _1, \ldots , \lambda _n\) in the above polynomial divided by n!.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Auburn University Montgomery, Montgomery, AL, 36124, USA

    Tianran Chen

  2. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Robert Davis

Authors
  1. Tianran Chen
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  2. Robert Davis
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Correspondence to Tianran Chen .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA

    Jörg Feldvoss

  2. Department of Mathematics, Spring Hill College, Mobile, AL, USA

    Lauren Grimley

  3. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA

    Drew Lewis

  4. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA

    Andrei Pavelescu

  5. Department of Mathematics and Statistics, University of South Alabama, Mobile, AL, USA

    Cornelius Pillen

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Chen, T., Davis, R. (2019). A Product Formula for the Normalized Volume of Free Sums of Lattice Polytopes. In: Feldvoss, J., Grimley, L., Lewis, D., Pavelescu, A., Pillen, C. (eds) Advances in Algebra. SRAC 2017. Springer Proceedings in Mathematics & Statistics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-030-11521-0_6

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