15 citations · 79 across the 28 of their papers we have counts for
5 papers · 1 filter
Parametrized topological complexity of collision-free motion planning in the plane
Daniel C. Cohen, Michael Farber, Shmuel Weinberger
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as…
Generating functions and topological complexity
Michael Farber, Daisuke Kishimoto, Donald Stanley
We examine the rationality conjecture which states that (a) the formal power series $\sum_{r\ge 1} \tc_{r+1}(X)\cdot x^r$ represents a rational function of with a single pole o…
The Rado Simplicial Complex
Michael Farber, Lewis Mead, Lewin Strauss
A Rado simplicial complex X is a generalisation of the well-known Rado graph. X is a countable simplicial complex which contains any countable simplicial complex as its induced sub…
Topological embeddings into random 2-complexes
Michael Farber, Tahl Nowik
We consider 2-dimensional random simplicial complexes in the multi-parameter model. We establish the multi-parameter threshold for the property that every 2-dimensional simplic…
Random Surfaces with Boundary
Chaim Even-Zohar, Michael Farber
A surface with boundary is randomly generated by gluing polygons along some of their sides. We show that its genus and number of boundary components asymptotically follow a bivaria…