  We address the Leader Election (LE) problem in networks of anonymous sensors
sharing no kind of common coordinate system. Leader Election is a fundamental
symmetry breaking problem in distributed computing. Its goal is to assign value
1 (leader) to one of the entities and value 0 (non-leader) to all others. In
this paper, assuming n > 1 disoriented anonymous sensors, we provide a complete
charac- terization on the sensors positions to deterministically elect a
leader, provided that all the sensors' positions are known by every sensor.
More precisely, our contribution is twofold: First, assuming n anonymous
sensors agreeing on a common handedness (chirality) of their own coordinate
system, we provide a complete characterization on the sensors positions to
deterministically elect a leader. Second, we also provide such a complete
chararacterization for sensors devoided of a common handedness. Both
characterizations rely on a particular object from combinatorics on words,
namely the Lyndon Words.
