Integer sequences and matrices over finite fields
Kent E. Morrison
TL;DR
This paper compiles and explains various integer sequences counting matrices over finite fields, linking them to OEIS and providing proofs and generating functions for these sequences.
Contribution
It offers a comprehensive collection of sequences, formulas, and proofs related to matrices over finite fields, with references to existing literature and OEIS entries.
Findings
Sequences and generating functions for matrices over finite fields
Cycle index as a key tool in derivations
References to OEIS entries for these sequences
Abstract
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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Taxonomy
TopicsCoding theory and cryptography · Graph theory and applications · graph theory and CDMA systems