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the pair diagram


  
Figure: The de Bruijn diagram of a (3,1/2) automaton has three vertices, so the pair diagram for ordered pairs has 9 vertices. Sometimes it is useful to draw the pair diagram for unordered pairs.
\begin{figure} \centering \begin{picture} (140,120) \put(0,0){\epsfxsize=140pt \epsffile{3hpair.eps}} \end{picture} \end{figure}

Vertices in the pair diagram are pairs of vertices from the base diagram. Vertices are linked if all matching members of the pairs are linked, and with the same label, at that. Similar definitions apply to triple diagrams and so on. The connection matrix of the pair diagram is the second moment matrix of the de Bruijn fragments.


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2000-03-17