Visual Representation
Cobham contributed work relating Prouhet's work with finite automata. A mathematical graph is made of edges and nodes. With finite automata, the edges are labeled with a letter in an alphabet. To use the graph, one starts at a node and travels along the edges to reach a final node. The path taken along the graph forms the word. It is a finite graph because there are a countable number of nodes and edges, and only one path connects two distinct nodes.
Gauss codes, created by Carl Friedrich Gauss in 1838, are developed from graphs. Specifically, a closed curve on a plane is needed. If the curve only crosses over itself a finite number of times, then one labels the intersections with a letter from the alphabet used. Traveling along the curve, the word is determined by recording each letter as an intersection is passed. Gauss noticed that the distance between when the same symbol shows up in a word is an even integer.
Read more about this topic: Combinatorics On Words
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