论文标题
宇宙室的面孔
Faces of Cosmological Polytopes
论文作者
论文摘要
宇宙学是由Arkani-Hamed，Benincasa和Postnikov引入的晶格多层，并在一类宇宙学模型中研究了宇宙的波函数。更具体地说，它们为任何Feynman图（即无向图）构造了宇宙学的多层。在本文中，我们启动了这些多面体的组合研究。我们对他们的面孔进行完整的描述，确定不是简单的最小面孔，并在特定情况下计算面孔的数量。特别是，我们对树木的宇宙学杂志的$ f $ vector进行了递归描述。
A cosmological polytope is a lattice polytope introduced by Arkani-Hamed, Benincasa, and Postnikov in their study of the wavefunction of the universe in a class of cosmological models. More concretely, they construct a cosmological polytope for any Feynman diagram, i.e. an undirected graph. In this paper, we initiate a combinatorial study of these polytopes. We give a complete description of their faces, identify minimal faces that are not simplices and compute the number of faces in specific instances. In particular, we give a recursive description of the $f$-vector of cosmological polytopes of trees.
