2022/09/16 by Lukas Kühne, Kühne, Lukas, Leonid Monin +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Graph Labeling and Dimension Problems #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2209.08069
openalex publication_date 2022/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.