Abstract

ARDILA, Federico; BECK, Matthias  and  MCWHIRTER, Jodi. The arithmetic of Coxeter permutahedra. Rev. acad. colomb. cienc. exact. fis. nat. [online]. 2020, vol.44, n.173, pp.1152-1166.  Epub July 08, 2021. ISSN 0370-3908.  https://doi.org/10.18257/raccefyn.1189.

Ehrhart theory measures a polytope P discretely by counting the lattice points inside its dilates P, 2P, 3P, We compute the Ehrhart theory of four families of polytopes of great importance in several areas of mathematics: the standard Coxeter permutahedra for the classical Coxeter groups A n , B n , C n , Dn. A central tool, of independent interest, is a description of the Ehrhart theory of a rational translate of an integer projection of a cube.

Keywords : Polytope; Ehrhart theory; Coxeter group; Permutahedron; Tree; Lambert function.

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