2024/04/05 by Vadym Kurylenko, Kurylenko, Vadym
Mathematics · Engineering · Computer Science · #Mathematics and Applications #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Digital Image Processing Techniques
paper · pdf · doi:10.48550/arxiv.2404.03975
The local h^*-polynomial is a natural invariant of a lattice polytope appearing in Ehrhart theory and Hodge theory. In this work, we study the question posed in [GKZ94] concerning the classification of lattice simplices with vanishing local h^*-polynomial. Such simplices are called thin. We relate this question to linear codes and hyperplane arrangements over finite rings. This allows us to obtain a complete classification of the 4-dimensional thin simplices, extending the previously known results in dimensions up to 3.