To: Steve Krantz
From: Doron Zeilberger
Bcc: DZ's E-mailing list + Notices Editor
A Copy is also posted as appendix to my Opinion 18
Re: Nah-Nah-Nah-Nugah, Guess Who is publishing in
a `Substandard' Free Electronic Journal?
Dear Steve,
Please show the piece below to your retarded dean!
In case you forgot, S. -T. Yau won the Fiedls Medal,
(and Fan Chung should have!)
Best wishes
Doron
---------From ElJC------
From ejc@math.gatech.edu Fri Feb 12 09:36:02 1999
The following paper has been published in The Electronic Journal of
Combinatorics:
Fan Chung and S.-T. Yau
Coverings, Heat Kernels and Spanning Trees
It is R12 of Volume 6(1), and can be viewed at
.
Abstract: We consider a graph $G$ and a covering $\tilde{G}$
of $G$ and we study the relations of their eigenvalues and
heat kernels. We evaluate the heat kernel for an infinite
$k$-regular tree and we examine the heat kernels for general
$k$-regular graphs. In particular, we show that a $k$-regular
graph on $n$ vertices has at most
\[ (1+o(1)) \frac {2\log n}{kn \log k}
\left( \frac{(k-1)^{k-1}} {(k^2-2k)^{k/2-1}}\right)^n \]
spanning trees, which is best possible within a constant factor.
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