[seqfan] Re: Partition into Stroke of Graph

[Chris Scussel]

Hello all,

? ? The OEIS entry for A089243 gives this example for a(3):

? ? ? ? ?{1->0->2, 0->3}
? ? ? ? ?{1->0->2, 3->0}
? ? ? ? ?{1->0, 2->0, 3->0}
? ? ? ? ?{0->1, 0->2, 0->3}

and concludes that a(3)=4.

? ? Yasutoshi's version of a(3) is:

? ? ? ? ? 301+02 ?301+20 ?102+03 ?102+30 ?203+01 ?203+10
? ? ? ? ? 103+02 ?103+20 ?201+03 ?201+30 ?302+01 ?302+10
? ? ? ? ? 01+02+03 ?10+20+30

and so gets a(3)=14. It appears to me that OEIS's version
is treating the star graph as unlabeled, so that

? ? ? ? ? {1->0->2, 0->3}
? ? ? ? ? {1->0->3, 0->2}
? ? ? ? ? {2->0->1, 0->3}
? ? ? ? ? {2->0->3. 0->1}
? ? ? ? ? {3->0->1, 0->2}
? ? ? ? ? {3->0->2, 0->1}

all represent the same partition, while Yasutoshi's version?
considers them distinct. ?The other OEIS partition into two
parts also maps to six of Yasutoshi's partitions. This accounts
for the difference between OEIS's a(3)=4 and Yasutoshi's a(3)=14.

? ? Since the sequence has its origin in writing Japanese Kanji
I can understand why Yasutoshi would consider the star graph
to be labeled. ?If I have understood this correctly, perhaps
a second sequence is needed.


? ? ?Chris
?