Z_n Homometry

C algorithm for brute-force enumeration of homometric sets in the cyclic groups Z_n

See the paper Jedrzejewski F., Johnson T. (2013) The Structure of Z-Related Sets. In: Yust J., Wild J., Burgoyne J.A. (eds) Mathematics and Computation in Music. MCM 2013. Lecture Notes in Computer Science, vol 7937. Springer, Berlin, Heidelberg for more theoretical information.

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Compile the C program with gcc and start:

>>> ./Zn_homomenumerate n p output_file

where

• n is an integer defining the order of the Z_n cyclic group
• p is an integer defining the cardinality of the subsets of Z_n to be examined.
• output_file is the name of the output file to be written

For example:

>>> ./Zn_homomenumerate 16 6 output.txt

Use the python script to count the unique homometric n-uples:

>>> python Zn_homomcounts.py output.txt

With the above example:

>>> python Zn_homomcounts.py output.txt
# of homometric subsets
2-uples: 28
3-uples: 3

The zip file enumeration_results.zip contains an enumeration of homometric subsets for cyclic groups Z_n of order up to 28.