Stroke sequence

[kohmoto]

    Hi, Seqfans.

    I explane with an easy example.

         Star graph with four edges.
　


         .__|__.
         .....|__.

         Names of nodes.

         *1*
         402
         *3*

         Partitions into strokes :
         103+402, 102+403, 102+304, 103+02+04, 103+20+40, 102+03+04, 
102+30+40, 10+20+30+40, 01+02+03+04, so a(4)=9

         Where "103+402" means a partition into directed paths {103,402} of 
a di-graph {10,02,03,40}
         c.1. 103 and 402 have no common edge
         c.2. Sum of 103 and 402 doesn't become a di-path
         Hence the partition is a partition into strokes.

         For example   a partition {103,40,02} of {10,02,03,40} is not a 
partition into strokes, because it doesn't satisfy c.2 as follows.
         Sum of 40 and 02 becomes a directed path.

         Partitions 102+403 and 104+203 are a reflection each other, so they 
are the same partition into strokes of a star graph.


        Max wrote.
         >in the example we see edges of both directions, e.g., 1->0 and 
0->1 which is very confusing.
         {1->0,2->0,3->0} and {0->1,0->2,0->3} are diferent partitions. 1->0 
and 0->1 don't exist on the same graph.

         >In the example I see two partitions  {1->0, 2->0, 3->0} and {0->1, 
0->2, 0->3} that looks like reflections of one another, aren't they?
         It is not a reflection. Compare with the example which I described.

    Yasutoshi
 
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