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On Volumes of Permutation Polytopes

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Discrete Geometry and Optimization

Part of the book series: Fields Institute Communications ((FIC,volume 69))

Abstract

This paper focuses on determining the volumes of permutation polytopes associated to cyclic groups,dihedral groups, groups of automorphisms of tree graphs, and Frobenius groups. We do this through the use of triangulations and the calculation of Ehrhart polynomials. We also briefly discuss the theta body hierarchy of various permutation polytopes.

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Acknowledgements

We would like to thank Igor Pak, David Perkinson, Raman Sanyal, Bernd Sturmfels, and Rekha Thomas for helpful discussions. We are grateful to two anonymous referees who gave us many useful corrections and suggestions that improved the paper. The three authors were partially supported by NSF grant DMS-0914107. The first and second authors were supported by VIGRE NSF grant DMS-0636297. The third author was partially supported by NSERC Postgraduate Scholarship 281174. The second author is grateful to the Fields Institute for its hospitality and support during his visit.

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Authors and Affiliations

  1. Department of Mathematics, University of California, One Shields Ave., Davis, CA, 95616, USA

    Katherine Burggraf & Jesús De Loera

  2. Department of Mathematics, California Institute of Technology, Mathematics 253-37, Pasadena, CA, 91125, USA

    Mohamed Omar

Authors
  1. Katherine Burggraf
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  2. Jesús De Loera
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  3. Mohamed Omar
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Corresponding author

Correspondence to Jesús De Loera .

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Editors and Affiliations

  1. , Mathematics & Statistics, University of Calgary, University Drive NW, Calgary, T2N 1N4, Alberta, Canada

    Karoly Bezdek

  2. , Department of Computing, McMaster University, Main Street West 1280, Hamilton, L8S 4K1, Ontario, Canada

    Antoine Deza

  3. School of Engineering, Department of Management Science and Eng, Stanford University, Via Ortega 475, Stanford, 94305, California, USA

    Yinyu Ye

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Burggraf, K., De Loera, J., Omar, M. (2013). On Volumes of Permutation Polytopes. In: Bezdek, K., Deza, A., Ye, Y. (eds) Discrete Geometry and Optimization. Fields Institute Communications, vol 69. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00200-2_5

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