On Volumes of Permutation Polytopes

  • Katherine Burggraf
  • Jesús De Loera
  • Mohamed Omar
Chapter
First Online:
Part of the Fields Institute Communications book series (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.

Key words

Permutation polytopes Birkhoff’s polytope Volumes Ehrhart polynomials Gale duality Triangulations Theta bodies 

Subject Classifications

52A38 52B20 52B35 
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Notes

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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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Katherine Burggraf
    • 1
  • Jesús De Loera
    • 1
  • Mohamed Omar
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA
  2. 2.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

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