English

Scalar $q$-subresultants and Dickson matrices

Combinatorics 2020-09-17 v1 Rings and Algebras

Abstract

Following the ideas of Ore and Li we study qq-analogues of scalar subresultants and show how these results can be applied to determine the rank of an Fq\mathbb{F}_q-linear transformation ff of Fqn\mathbb{F}_{q^n}. As an application we show how certain minors of the Dickson matrix D(f)D(f), associated with ff, determine the rank of D(f)D(f) and hence the rank of ff.

Keywords

Cite

@article{arxiv.1909.06409,
  title  = {Scalar $q$-subresultants and Dickson matrices},
  author = {Bence Csajbók},
  journal= {arXiv preprint arXiv:1909.06409},
  year   = {2020}
}
R2 v1 2026-06-23T11:14:55.823Z