Appears in collection : 2022 - T3 - WS2 - Geometry, Topology and Statistics in Data Sciences

The chromatic Delaunay mosaic of $s+1$ finite sets in d dimensions is an (s+d)-dimensional Delaunay mosaic that represents the individual sets as well as their interactions. For example, it contains a (non-standard) dual of the overlay of the Voronoi tessellations of any subset of the $s+1$ colors. We prove bounds on the size of the chromatic Delaunay mosaic, in the worst and average case, and suggest how to use image, kernel, and cokernel persistence to get stable diagrams describing the interaction of the points of different colors.

Acknowledgements. This is incomplete and ongoing joint work with Ranita Biswas, Sebastiano Cultrera, Ondrej Draganov, and Morteza Saghafian, all at IST Austria.