Juggling braids and links
Using a simplistic model of juggling based on physics, a natural map is constructed from the set of periodic juggling patterns (or site swaps) to links. We then show that all topological links can be juggled.
math.GT↗
arXiv subjects
Satyan L. Devadoss
Publications and source records attributed to Satyan L. Devadoss.
Coxeter Complexes and Graph-Associahedra
Given a graph G, we construct a simple, convex polytope whose face poset is based on the connected subgraphs of G. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial Coxeter system, the minimal blow-ups of its associated Coxeter complex has a tiling by graph-associahedra. The geometric and combinatorial properties of the complex as well as of the polyhedra are given. These spaces are natural generalizations of the Deligne-Knudsen-Mumford compactification of the real moduli space of curves.
math.QA↗
Compatible Triangulations and Point Partitions by Series-Triangular Graphs
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to improve the upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets. The problem is generalized to finding compatible triangulations for more than two point sets and we show that such triangulations can be constructed with only a linear number of Steiner points added to each point set.
cs.CG↗
Combinatorial equivalence of real moduli spaces
A well-known construction of associahedra comes from truncations of simplices. Motivated by compactifications of point configurations, we show associahedra as truncations of certain products of simplices. This is then used to provide a combinatorial construction of the real moduli space of spheres relating it to blow-ups of the braid hyperplane arrangement.
math-ph↗
A space of cyclohedra
The real points of the Deligne-Knudsen-Mumford moduli space of marked points on the sphere has a natural tiling by associahedra. We extend this idea to create a moduli space tiled by cyclohedra. We explore the structure of this space, coming from blow-ups of hyperplane arrangements, as well as discuss possibilities of its role in knot theory and mathematical physics.
math.QA↗
Cellular Structures determined by Polygons and Trees
The polytope structure of the associahedron is decomposed into two categories, types and classes. The classification of types is related to integer partitions, whereas the classes present a new combinatorial problem. We solve this and incorporate the results into properties of the real moduli space of Riemann spheres. Connections are discussed with relation to classic combinatorial problems as well as to other sciences.
math.CO↗
Tessellations of Moduli Spaces and the Mosaic Operad
We construct a new (cyclic) operad of `mosaics' defined by polygons with marked diagonals. Its underlying (aspherical) spaces are the sets of real points of the moduli space of punctured Riemann spheres, which are naturally tiled by Stasheff associahedra. We (combinatorially) describe them as iterated blow-ups and show that their fundamental groups form an operad with similarities to the operad of braid groups.
math.AG↗