Takenings, rames and mills : structures for the modelling of branching

摘要

A takening is a combinatorial structure composed of points and rays. A ray is a finite sequence of at least two points, and two rays have at most one point in common, which must be the foot (initial point) of at least one of them. Walks, paths, proper walks and cycles are defined. A root is a point which is the foot of every ray on which it lies. Every connected takening is either a rame, which has one root and no cycle, or a mill, which has one cycle and no root. The concept of a subtakening is defined.