D_2n Homometry

C algorithm for brute-force enumeration of homometric sets in the dihedral groups D_2n

See the paper Genuys G., Popoff A. (2017) Homometry in the Dihedral Groups: Lifting Sets from ℤn to Dn. In: Agustín-Aquino O., Lluis-Puebla E., Montiel M. (eds) Mathematics and Computation in Music. MCM 2017. Lecture Notes in Computer Science, vol 10527. Springer, Cham for more theoretical information.

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Compile the C program with gcc and start:

>>> ./D2n_homomenumerate n p output_file

where

n is an integer defining the order of the D_2n dihedral group
p is an integer defining the cardinality of the subsets of D_2n to be
```
examined.
```
output_file is the name of the output file to be written

For example:

>>> ./D2n_homomenumerate 12 5 output.txt

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

>>> python D2n_homomcounts.py output.txt

With the above example:

>>> python D2n_homomcounts.py
# of left homometric subsets
2-uples: 8
3-uples: 2
# of simultaneous left and right homometric subsets
2-uples: 8
3-uples: 2

The zip file partial_results.zip contains a partial enumeration of subsets of cardinality p in the dihedral groups D_2n, for p=4,5,6,7 and n from 8 to 18.