Related papers: Amplitubes: Graph Cosmohedra
Discrete homotopy theory or A-homotopy theory is a combinatorial homotopy theory defined on graphs, simplicial complexes, and metric spaces, reflecting information about their connectivity. The present paper aims to further understand the…
Tropicalization is a procedure for associating a polyhedral complex in Euclidean space to a subvariety of an algebraic torus. We study the question of which graphs arise from tropicalizing algebraic curves. By using Baker's specialization…
We consider semi-algebraic subsets of the Grassmannian of lines in three-space called tree amplituhedra. These arise in the study of scattering amplitudes from particle physics. Our main result states that tree amplituhedra in ${\rm…
We show that accordiohedra furnish polytopes which encode amplitudes for all massive scalar field theories with generic interactions. This is done by deriving integral formulae for the Feynman diagrams at tree level and integrands at one…
Cosmological polytopes of graphs are a geometric tool in physics to study wavefunctions for cosmological models whose Feynman diagram is given by the graph. After their recent introduction by Arkani-Hamed, Benincasa and Postnikov the focus…
An ordinary voltage graph embedding of a graph in a surface encodes a certain kind of highly symmetric covering space of that surface. Given an ordinary voltage graph embedding of a graph $G$ in a surface with voltage group $A$ and a…
Flow polytopes of acyclic oriented graphs arise naturally in combinatorial optimization, and the study of their volumes and triangulations has revealed intriguing connections across combinatorics, geometry, algebra, and representation…
We continue the study of open associahedra associated with bi-color scattering amplitudes initiated in arXiv:1912.08307. We focus on the facet geometries of the open associahedra, uncovering many new phenomena such as fiber-product…
In this series, we introduce and investigate the concept of connectoids, which captures the connectivity structure of various discrete objects such as undirected graphs, directed graphs, bidirected graphs, hypergraphs and finitary matroids.…
In this paper, we introduce a new method to compute magnitude homology of general graphs. To each direct sum component of magnitude chain complexes, we assign a pair of simplicial complexes whose simplicial chain complex is isomorphic to…
A novel self-assembly strategy for polypeptide nanostructure design was presented in [Design of a single-chain polypeptide tetrahedron assembled from coiled-coil segments, Nature Chemical Biology 9 (2013) 362--366]. The first mathematical…
This article aims to propose a novel analytical model for anisotropic multi-layer elliptical structures incorporating graphene layers. The multi-layer structure is formed of various magnetic materials. An external magnetic bias has been…
Given a polyhedron (planar, $3$-connected graph) $G$, we investigate its common neighbourhood graph con($G$). For cubic ($3$-regular) polyhedra, we show that the planarity of con($G$) depends on the number of odd faces of $G$, and on their…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
The $k$-associahedron $Ass_k(n)$ is the simplicial complex of $(k+1)$-crossing-free subgraphs of the complete graph with vertices on a circle. Its facets are called $k$-triangulations. We explore the connection of $Ass_k(n)$ with the…
In this paper, we explore the applicability of the BCFW-like recursion relations \cite{He:2018svj,Yang:2019esm} to a wider class of positive geometries. Previously it was found in \cite{Jagadale:2022rbl}, the tree level scattering amplitude…
Much information about a graph can be obtained by studying its spanning trees. On the other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question of developing a theory of trees in higher dimension. As observed…
We explore several families of flip-graphs, all related to polygons or punctured polygons. In particular, we consider the topological flip-graphs of once-punctured polygons which, in turn, contain all possible geometric flip-graphs of…
An elimination tree for a connected graph $G$ is a rooted tree on the vertices of $G$ obtained by choosing a root $x$ and recursing on the connected components of $G-x$ to produce the subtrees of $x$. Elimination trees appear in many guises…
We show that the F-theory dual of the heterotic string with unbroken Spin(32)/Z_2 symmetry in eight dimensions can be described in terms of the same polyhedron that can also encode unbroken E_8\times E_8 symmetry. By considering particular…