Techniques in equivariant Ehrhart theory [article]

Sophia Elia, Donghyun Kim, Mariel Supina
2022 arXiv   pre-print
Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action. We present a catalogue of techniques with applications in this field, including zonotopal decompositions, symmetric triangulations, combinatorial interpretation of the h^∗-polynomial, and certificates for the (non)existence of invariant non-degenerate hypersurfaces. We apply these methods to several families of examples including
more » ... es, orbit polytopes, and graphic zonotopes, expanding the library of polytopes for which their equivariant Ehrhart theory is known.
arXiv:2205.05900v1 fatcat:aizfrbxebjedphtmxfdoqfz7tu