[seqfan] Re: A conjecture concerning connected rooted strength 1 Eulerian graphs with n nodes

[Richard Mathar]

rjm> From seqfan-bounces at list.seqfan.eu Thu Mar 12 18:05:35 2009
rjm> From: Richard Mathar <mathar at strw.leidenuniv.nl>
rjm> Date: Thu, 12 Mar 2009 17:27:32 +0100
rjm> To: seqfan at seqfan.eu
rjm> Subject: [seqfan] Re: A conjecture concerning connected rooted strength 1 Eulerian graphs with n nodes
rjm> 
rjm> If "E" is the Euler transform we have
rjm> 
rjm> A001349 -> E-> A000088
rjm> 
rjm> A003049 -> E-> A002854
rjm> 
rjm> So to show that 
rjm> A158007 -> E -> A007126
rjm> 
rjm> you can equivalently show that A000088+A002854=A007126.
rjm> My graph theoretical background is too weak to address that
rjm> question.
rjm> 

Vladeta points out that the Euler transform is not a linear transform,
so unfortunately summation/subtraction on the source side does
not imply summation/subtraction on the image side (at least not without
a detour via logarithms of generating functions).

To my deep regret, I have to withdraw this beautiful, but wrong analysis.
---I think it is Murphy's law which says that deep questions
have short, easy to understand, but unfortunately wrong answers...

RJM