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Integer sequences and matrices over finite fields. (English) Zbl 1102.05006
Summary: 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.

MSC:
05A15 Exact enumeration problems, generating functions
11B83 Special sequences and polynomials
15B33 Matrices over special rings (quaternions, finite fields, etc.)
05A10 Factorials, binomial coefficients, combinatorial functions
05A30 \(q\)-calculus and related topics
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