Geodesic
Counting toroidal binary arrays. II.
Journal of integer sequences, Tome 18 (2015) no. 8
We derive formulas for (i) the number of distinct toroidal $n \times n$ binary arrays, allowing rotation of rows and/or columns as well as matrix transposition, and (ii) the number of distinct toroidal $n \times n$ binary arrays, allowing rotation and/or reflection of rows and/or columns as well as matrix transposition.
Classification : 05A05
Keywords: toroidal array, Euler's phi function, group action, orbit, Pólya's enumeration theorem 
@article{JIS_2015__18_8_a6,
     author = {Ethier,  S.N. and Lee,  Jiyeon},
     title = {Counting toroidal binary arrays. {II.}},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {8},
     zbl = {1320.05006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a6/}
}
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Ethier,  S.N.; Lee,  Jiyeon. Counting toroidal binary arrays. II.. Journal of integer sequences, Tome 18 (2015) no. 8. http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a6/