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Integer sequences and matrices over finite fields

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arxiv math/0606056 v1 pith:W2R5MJAU submitted 2006-06-02 math.CO

Integer sequences and matrices over finite fields

classification math.CO
keywords sequencesintegermatricescontainsfieldsfinitefunctionsgenerating
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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 (OEIS). 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.

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  1. Expressivity of Shallow Neural Networks Over Finite Fields

    math.AG 2026-07 accept novelty 7.0

    For shallow polynomial networks over finite fields, the representable-function count is computed exactly for (n,1,k) and (n,2,k), and collapses to a linear-matrix count when the activation degree is a power of the fie...