Lattice polytopes, finite abelian subgroups in \SL(n,\C) and coding theory

2013/09/20 by Batyrev, Victor, Hofscheier, Johannes
#52B20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.5312

Abstract

We consider d-dimensional lattice polytopes Δ with h^*-polynomial h^*_Δ=1+h_k^*t^k for 1 2, the main technical tool in the classification of these linear codes is the non-vanishing theorem for generalized Bernoulli numbers B_1,χ^(r) associated with odd characters χ:\F_q^*→\C^* where q=p^r. Our result implies a complete classification of all lattice polytopes whose h^*-polynomial is a binomial.

Related

• Lattice point enumeration of polytopes associated to integer compositions
• Lattice polytopes with a given h^*-polynomial
• Thin polytopes: Lattice polytopes with vanishing local h^*-polynomial
• Lattices from codes over ℤ_q: Generalization of Constructions D, D' and D
• Thin Simplices via Modular Arithmetic