Alcoved Polytopes II

  • Thomas LamEmail author
  • Alexander Postnikov
Part of the Progress in Mathematics book series (PM, volume 326)


This is the second of two papers where we study polytopes arising from affine Coxeter arrangements. Our results include a formula for their volumes, and also compatible definitions of hypersimplices, descent numbers and major index for all Weyl groups. We give a q-analogue of Weyl’s formula for the order of the Weyl group. For An, Cn and D4, we give a Gröobner basis which induces the triangulation of alcoved polytopes.


Convex polytopes affine Weyl group hypersimplex 

Mathematics Subject Classification (2010):

Primary 52B Secondary 05A05 20F55 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsM.I.T., CambridgeCambridgeUSA

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