We study the Ricci curvature of Hasse diagrams Bruhat order finite irreducible Coxeter groups. For this purpose we compute maximum degree these graphs for types B n and D . The proof uses a new graph Γ ( π ) defined any element in corresponding group.

Hypergraphs serve as models of complex networks that capture more general structures than binary relations. For graphs, a wide array statistics has been devised to gauge different aspects their structures. lack behind in this respect. The Forman–Ricci curvature is for graphs based on Riemannian geometry, which stresses the relational character vertices network by focusing edges rather vertices....

tournaments are a type of directed graph which have been used to study the geometry classical flag manifolds. We became interested in this graphs because combinatorial properties can be geometric [21]introduced Forman-Ricci curvature for and undirected hypergraphs obtained as particular case. In work we present basic ideas about Forman- Ricci graphs, characterize parabolic terms calculate any t...

We express the discrete Ricci curvature of a graph as minimal eigenvalue family matrices, one for each vertex whose entries depend on local adjacency structure graph. Using this method we compute or bound Cayley graphs finite Coxeter groups and affine Weyl groups. As an application obtain isoperimetric inequality that holds all

We use the recent discovered x−ψ duality to parameterize spacetime in terms of wave functions and quantum prepotentials. The components of metric, connection, curvature, Ricci tensor and scalar curvature as well as Einstein equations in this parameterization are

We define a notion of a measured length space X having nonnegative N -Ricci curvature, for N ∈ [1,∞), or having ∞-Ricci curvature bounded below by K, for K ∈ R. The definitions are in terms of the displacement convexity of certain functions on the associated Wasserstein metric space P2(X) of probability measures. We show that these properties are preserved under measured Gromov-Hausdorff limits...