Example in A Free Group
Suppose that F is the free group on the two element set . A word w in the symmetric generating set is said to be reduced if the letters do not occur next to each other in w, nor do the letters . Every element is represented by a unique reduced word, and this reduced word is the shortest word representing g. For example, since the word is reduced and has length 2, the word norm of equals 2, so the distance in the word norm between and equals 2. This can be visualized in terms of the Cayley graph, where the shortest path between b and a has length 2.
Read more about this topic: Word Metric
Famous quotes containing the words free and/or group:
“I believe that man is in the last resort so free a being that his right to be what he believes himself to be cannot be contested.”
—G.C. (Georg Christoph)
“Instead of seeing society as a collection of clearly defined “interest groups,” society must be reconceptualized as a complex network of groups of interacting individuals whose membership and communication patterns are seldom confined to one such group alone.”
—Diana Crane (b. 1933)