Theory of linear and integer programming
Theory of linear and integer programming
Unimodular Triangulations and Coverings of Configurations Arising from Root Systems
Journal of Algebraic Combinatorics: An International Journal
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Let Gn be the complete graph on the vertex set [n] = {1, 2, ..., n} and ω an orientation of Gn, i,e., ω is an assignment of a direction i → j of each edge {i, j} of Gn. Let eq denote the qth unit coordinate vector of Rn. Write P(Gn;ω) ⊂ Rn for the convex hull of the (n 2) points ei - ej, where i → j is the direction of the edge {i, j} in the orientation ω. It will be proved that, for n ≥ 5, the Ehrhart ring of the convex polytope P(Gn;ω) is Gorenstein if and only if (Gn;ω) possesses a Hamiltonian cycle, i.e., a directed cycle of length n.