论文标题
广义固定的多层代数
The polytope algebra of generalized permutahedra
论文作者
论文摘要
地位的变形的多层亚代理可以在相应的超平面排列的山雀代数上赋予模块的结构。我们探索了这种构建，并在（b）广义定义下（签名）排列（签名）排列（签名）排列之间的统计数据之间存在关系。在B型中，模块结构令人惊讶地揭示了B型B型的通用定居者的任何发电机（通过签名的Minkowski总和）都将包含至少$ 2^{d-1} $全尺寸多型。我们发现，最低限度的一系列简单家族。最后，我们证明定义多层代数的关系与广义定位的HOPF单体结构兼容。
The polytope subalgebra of deformations of a zonotope can be endowed with the structure of a module over the Tits algebra of the corresponding hyperplane arrangement. We explore this construction and find relations between statistics on (signed) permutations and the module structure in the case of (type B) generalized permutahedra. In type B, the module structure surprisingly reveals that any family of generators (via signed Minkowski sums) for generalized permutahedra of type B will contain at least $2^{d-1}$ full-dimensional polytopes. We find a generating family of simplices attaining this minimum. Finally, we prove that the relations defining the polytope algebra are compatible with the Hopf monoid structure of generalized permutahedra.
