论文标题
ehrhart理论中的技术
Techniques in equivariant Ehrhart theory
论文作者
论文摘要
ehrhart理论概括了晶格点枚举的研究，以解决线性群体作用下多层的对称性。我们介绍了该领域中应用的技术目录，包括$ H^\ ast $ - 多聚类的$ H^\ ast $ polynomial的对称分解，对称三角形，对（非）不变的非分数超级表情的证书。我们将这些方法应用于几个示例家族，包括超图像，轨道多面体和图形地位，扩展了其ehrhart理论的多型库。
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 $h^\ast$-polynomial, and certificates for the (non)existence of invariant non-degenerate hypersurfaces. We apply these methods to several families of examples including hypersimplices, orbit polytopes, and graphic zonotopes, expanding the library of polytopes for which their equivariant Ehrhart theory is known.
