Automated Counting and Statistical Analysis of Families of Spanning Trees

Automated Counting and Statistical Analysis of Families of Spanning Trees
By Yukun Yao and Doron Zeilberger

NOTE: THIS PROJECT HAS BEEN INCORPORATED AS PART OF THIS ARTICLE IT IS LEFT HERE FOR HISTORICAL REASONS.

.pdf .ps .tex

First Written: Nov. 15, 2018 .

Maple package

SpanningTrees.txt, a Maple package for automatically enunerating, and statistical analysis of spanning trees

JointConductance.txt, a Maple package for joint conductance .

Sample Input and Output for SpanningTrees.txt

If you want to see the rational generating functions enumerating the sequences enumerating the number of spanning trees in an m by n rectangular grid, as well asspanning forests, with application to joint conductance, for m from 2 to 5
the input file generates the output file.

If you want to see the rational generating functions enumerating the sequences enumerating the number of spanning trees in an m by n rectangular grid, for m from 2 to 6
the input file generates the output file.

Sample Input and Output for JointConductance.txt

If you want to see the rational generating functions enumerating the sequences enumerating the number of spanning trees in an m by n rectangular grid, for m from 2 to 7
the input file generates the output file.
Note that the generating functions for n ≤ 6 have been previously computed by Paul Raff and Faase, but m=7 seems to be new. Suprisingly, the degree of the denominator is 48, rather than 64 (until m=6 the degree is 2^m-1)

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