Typical output file: pu7.out
Remarks
- Some typical disclaimers and restrictions:
- These programs are provided with no warranty whatsoever.
- They are provided with the understanding that their use in anything
published or commercial will be properly acknowledged.
- They are provided with the understanding that they will not be
modified unless the modifications are documented and signed in the files.
- They are not "supported"; but if you find them interesting or useful,
fulling@math.tamu.edu will be delighted to hear from you and to provide
help as far as time and expertise permit.
- The maximum value of q (number of lines) has been set to
11 minus p (number of points). This parameter is intended to
be changed by the user. However, attempts to increase it significantly
may run into hardware limitations (see next point).
- For p > 3, printing of long and/or redundant output lines has
been suppressed to conserve memory. If you are using a notebook
front end, you may want to do this for p = 3 also. If necessary,
memory use could be optimized in these additional ways:
- Suppress the remaining output.
- Clear variables after their last use.
- Rewrite the programs to eliminate extra variables used for quantities
that are conceptually different but actually equal to others
(such as "linktriple" in pu4.m).
- Structure of the programs:
(The files are divided into these parts by blank lines. If you are
using a notebook front end, you should insert cell boundaries at these
places (at least) before executing. )
- Set up housekeeping and teach Mathematica how to reorder the
subscripted variables.
- Choose the maximum q and calculate the length of the corresponding
series.
- Construct a series for each possible configuration of line positions.
For example, "pyramid" in pu4.m represents 3 points
all joined to a fourth point by the same number of lines.
- Construct a series for each class of permutations.
- For labeled graphs this step is trivial, since only the identity
permutation needs to be considered. The one line of code is combined
with the next part of the program in that case.
- For unlabeled graphs, this is the most difficult part of the analysis,
and hard to explain without diagrams. Please consult Sec. 2.3 of the
paper and the cited pages in the book of Harary and Palmer. Each series
is a product of a series for each configuration of lines that forms
an orbit of the action of a canonical representative of the class.
- Construct the series for the entire generating function and manipulate
it into (relatively) readable form.
- Save the results to disk and exit.