Automatic Generation of Generating Functions for Enumerating Spanning Trees
By Pablo Blanco and Doron Zeilberger
.pdf (YET TO BE WRITTEN)
.tex
Written: April 2025
Maple package
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ExpSP.txt,
A maple package for computing generating functions enumerating the number of spanning trees in numerous
infinite familes of graphs.
Sample Input and Output for ExpSP.txt
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If you want to see the generating functions (that are always rational functions), in n, for the the number of spanning trees of the graphs
Hn,r defined in the paper, for 2 ≤ r ≤ 5, as well as generating functions for the "sum of the number of leaves"
over all spanning trees (that enables) computing the exact average number of leaves, as well as precise asymptotics
the input gives the
output
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If you want to see the generating functions (that are always rational functions), in n, for the the number of spanning trees of the graphs
Gn,r defined in the paper, for 2 ≤ r ≤ 5, as well as generating functions for the "sum of the number of leaves"
over all spanning trees (that enables) computing the exact average number of leaves, as well as precise asymptotics
the input gives the
output
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If you want to see the generating functions (that are always rational functions), in n, for the the number of spanning trees of the r by n
rectangular grid, for 2 ≤ r ≤ 4, as well as generating functions for the "sum of the number of leaves"
over all spanning trees (that enables) computing the exact average number of leaves, as well as precise asymptotics
the input gives the
output
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If you want to see JUST the generating functions (that are always rational functions), in n, for the the number of spanning trees of the r by n
rectangular grid, for 2 ≤ r ≤ 6
the input gives the
output
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If you want to see the generating functions (that are always rational functions), in n, for the the number of spanning trees of the r by n
rectangular torus, for 2 ≤ r ≤ 6, as well as generating functions for the "sum of the number of leaves"
over all spanning trees (that enables) computing the exact average number of leaves, as well as precise asymptotics
the input gives the
output
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If you want to see estimated statistics about the number of leaves in a random spanning tree of
Hn,r for various n and several r
the input gives the
output
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If you want to see estimated statistics about the number of leaves in a random spanning tree of
Gn,r for various n and several r
the input gives the
output
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If you want to see estimated statistics about the number of leaves in a random labeled tree on n vertices
for various n
the input gives the
output
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If you want to see a comparison of the exact average of the number of leaves in a random spanning trees
for our four favorite families,
See here