论文标题
碎片多面体
Shard polytopes
论文作者
论文摘要
对于排列弱点的任何晶格一致性，N。Reading证明，将属于同一一致性类别的编织风扇的锥粘合在一起，定义了一个完整的风扇，称为商风扇，V。Pilaud和F. Santos表明，它是Polytope的正常粉丝，称为PolyTope的正常风扇。在本文中，我们提供了一种更简单的方法来实现基于Minkowski基本多型的总和，称为shard polytopes，它们具有显着的组合和几何特性。与原始商的原始结构相反，这种Minkowski Sum方法扩展到$ b $。
For any lattice congruence of the weak order on permutations, N. Reading proved that gluing together the cones of the braid fan that belong to the same congruence class defines a complete fan, called a quotient fan, and V. Pilaud and F. Santos showed that it is the normal fan of a polytope, called a quotientope. In this paper, we provide a simpler approach to realize quotient fans based on Minkowski sums of elementary polytopes, called shard polytopes, which have remarkable combinatorial and geometric properties. In contrast to the original construction of quotientopes, this Minkowski sum approach extends to type $B$.
