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<DIV><FONT face="MS UI Gothic" size=2> Hi,
Seqfans. </FONT></DIV>
<DIV> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> I explane with an
easy example.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2>
</FONT></DIV>
<DIV><FONT face="MS UI Gothic"
size=2> Star graph with four
edges. <BR> <BR> </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> </FONT></DIV>
<DIV><FONT face="MS UI Gothic"
size=2>
.__|__.<BR>
.....|__.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic"
size=2> Names of
nodes.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic"
size=2>
*1*<BR>
402<BR> *3*
</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic"
size=2> Partitions into strokes
: <BR>
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 </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic"
size=2> Where "103+402" means a
partition into directed paths {103,402} of a di-graph
{10,02,03,40}<BR> c.1. 103 and
402 have no common edge<BR> c.2.
Sum of 103 and 402 doesn't become a di-path
<BR> Hence the partition is a
partition into strokes.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic"
size=2> 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.<BR> Sum of 40 and 02
becomes a directed path.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic"
size=2> Partitions 102+403 and
104+203 are a reflection each other, so th</FONT><FONT face="MS UI Gothic"
size=2>ey are the same partition into strokes of a star graph. </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic"
size=2> </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2>
Max wrote.</FONT></DIV>
<DIV><FONT face="MS UI Gothic"
size=2> >in the example we
see edges of both directions, e.g., 1->0 and 0->1 which is very
confusing.<BR>
{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.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic"
size=2> >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?<BR> It is not a
reflection. Compare with the example which I described. <BR></FONT><FONT
face="MS UI Gothic" size=2></FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> Yasutoshi</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2>
</DIV></FONT></FONT></DIV></BODY></HTML>