Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1

Integer Sequences and Matrices Over Finite Fields


Kent E. Morrison
Department of Mathematics
California Polytechnic State University
San Luis Obispo, CA 93407
USA

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. 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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(Concerned with sequences A002416 A002820 A002884 A005329 A006116 A006117 A006118 A006119 A006120 A006121 A006122 A015195 A015196 A015197 A015198 A015199 A015200 A015201 A015202 A015203 A015204 A015205 A015206 A015207 A015208 A015209 A015210 A015211 A015212 A015213 A015214 A015215 A015216 A015217 A022166 A022167 A022168 A022169 A022170 A022171 A022172 A022173 A022174 A022175 A022176 A022177 A022178 A022179 A022180 A022181 A022182 A022183 A022184 A022185 A022186 A022187 A022188 A053718 A053722 A053725 A053763 A053770 A053771 A053772 A053773 A053774 A053775 A053776 A053777 A053846 A053847 A053848 A053849 A053851 A053852 A053853 A053854 A053855 A053856 A053857 A053859 A053860 A053861 A053862 A053863 A069777 A070933 A076831 and A082877 .)

Received May 13 2005; revised version received February 10 2006. Published in Journal of Integer Sequences April 17 2006.

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