We provide a link between topological graph theory and pseudoline arrangements from the theory of oriented matroids. We investigate and generalize a function f that assigns to each simple pseudoline arrangement with an even number of elements a pair of complete-graph embeddings on a surface. Each element of the pair keeps the information of the oriented matroid we started with. We call a simple...

We apply periodic orbit theory to a two-dimensional nonintegrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing triangular deformation, it exhibits an astonishingly pronounced shell effect on its way through the shape transition. A semiclassical analysis reveals that this shel...

Let P be a graph property and r, s ∈ N, r ≥ s. A strong circular (P , r, s)-colouring of a graph G is an assignment f : V (G) → {0, 1, . . . , r − 1}, such that the edges uv ∈ E(G) satisfying |f(u) − f(v)| < s or |f(u) − f(v)| > r − s, induce a subgraph of G with the propery P . In this paper we present some basic results on strong circular (P , r, s)-colourings. We introduce the strong circula...

We show that any graph product of finitely generated groups is hierarchically hyperbolic relative to its vertex groups. apply this result answer two questions Behrstock, Hagen, and Sisto: we the syllable metric on forms a space, products are themselves This last strengthening Berlai Robbio by removing need for extra hypotheses groups.We also Genevois about geometry electrification finite

Abstract This paper shows that the operad encoding modular operads is Koszul. Using this result, we construct higher composition operations on (hairy) graph homology, which characterize its rational homotopy type.