Geodesic
Integer sequences and matrices over finite fields
Journal of integer sequences, Tome 9 (2006) no. 2
In this expository article we collect the integer sequences that count several different types of matrices over finite fields and provide references to the Online Encyclopedia of Integer Sequences. Section 1 contains the sequences, their generating functions, and examples. Section 2 contains the proofs of the formulas for the coefficients and the generating functions of those sequences if the proofs are not easily available in the literature. The cycle index for matrices is an essential ingredient in most of the derivations.
Classification : 05A15, 15A33, 05A10, 05A30, 11B65, 11B73
Keywords: integer sequences, matrices over finite fields, cycle index for matrices 
@article{JIS_2006__9_2_a2,
     author = {Morrison,  Kent E.},
     title = {Integer sequences and matrices over finite fields},
     journal = {Journal of integer sequences},
     year = {2006},
     volume = {9},
     number = {2},
     zbl = {1102.05006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2006__9_2_a2/}
}
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Morrison,  Kent E. Integer sequences and matrices over finite fields. Journal of integer sequences, Tome 9 (2006) no. 2. http://geodesic.mathdoc.fr/item/JIS_2006__9_2_a2/