This repo contains code that supports the paper "An enumeration of equilateral triangle dissections", Ales Drapal and Carlo Hamalainen, Discrete Applied Mathematics Volume 158, Issue 14, 28 July 2010, Pages 1479-1495. An open access (and more up to date version) is available on the arXiv: http://arxiv.org/abs/0910.5199

Carlo Hamalainen carlo.hamalainen@gmail.com

• dissections-clojure: Implementation in Clojure (for testing only)
• dissections-common-lisp: Implementation in Common Lisp (for testing only)
• dissections-cpp: Implementation in C++ (for actual enumeration runs)
• dissections-sage: Original implementation in Sage (useful for exploratory work)
• paper: Copy of the arXiv paper
• plot: Python script (uses PyX) for drawing triangle dissections
• spherical_bitrade_generator: Enumerator of spherical latin bitrades (uses "plantri")

To run the enumerator for order 18 with 5 slices, output going to /tmp/triangles/expt_18:

git clone https://github.com/carlohamalainen/triangle_dissections.git
cd triangle_dissections
make

If this fails due to not being able to find the Boost C++ library, set its location in triangle_dissections/dissections-cpp/Makefile and then re-run make in the top-level directory.

Now create a directory for this run of order 18 with 5 slices, and set up the Makefile which will run the main part of the enumeration:

cd dissections-cpp/example_run_directories

N=18
NRSLICES=5

SRCDIR=`pwd`

OUTPUT_DIRECTORY=/tmp/triangles/expt_$N

mkdir -p $OUTPUT_DIRECTORY
cd $OUTPUT_DIRECTORY
ln -s $SRCDIR/create_makefile.py
ln -s $SRCDIR/run_slice.sh
ln -s $SRCDIR/sort_and_merge_sigs.sh
ln -s $SRCDIR/uniq_sigs.sh

./create_makefile.py $SRCDIR/../.. $N $NRSLICES

To run the first part of the enumeration, use the Makefile with a suitable number of threads, say 14 on a 16 core PC:

make -j 14 # this would be at most the minimum of nr cores in PC and nr slices being produced

Once this finishes there will be $NRSLICES files of the form sigs_. To merge them into a single file containing a unique list of signatures, run the following script:

./sort_and_merge_sigs.sh $N

This will produce the file $OUTPUT_DIRECTORY/all_sigs_$N. This file can be used with post-processing scripts, or to answer simple questions like "how many dissections are there of order 18?":

cat all_sigs_$N | wc -l

The answer should be:

224708