Name
Title | ||
|---|---|---|
Block companion Singer cycles, primitive recursive vector sequences, and coprime polynomial pairs over finite fields. |
Abstract | ||
|---|---|---|
We discuss a conjecture concerning the enumeration of nonsingular matrices over a finite field that are block companion and whose order is the maximum possible in the corresponding general linear group. A special case is proved using some recent results on the probability that a pair of polynomials with coefficients in a finite field is coprime. Connection with an older problem of Niederreiter about the number of splitting subspaces of a given dimension are outlined and an asymptotic version of the conjectural formula is established. Some applications to the enumeration of nonsingular Toeplitz matrices of a given size over a finite field are also discussed. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.ffa.2011.02.008 | Finite Fields and Their Applications |
Keywords | DocType | Volume |
11T35,11T06,20G40,15B05 | Journal | 17 |
Issue | ISSN | Citations |
5 | 1071-5797 | 9 |
PageRank | References | Authors |
0.86 | 8 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sudhir R. Ghorpade | 1 | 80 | 12.16 |
| Samrith Ram | 2 | 20 | 3.52 |