Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields

Details Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields

2010-11-08

arxiv.org/abs/1011.1760v1

Journal of Combinatorial Theory, Series A, Vol. 118, No. 3 (2011), pp. 819-828

Mathematics

Combinatorics

10 pages; to appear in the Journal of Combinatorial Theory, Series A

Scientific paper

10.1016/j.jcta.2010.11.005

The probability for two monic polynomials of a positive degree n with coefficients in the finite field F_q to be relatively prime turns out to be identical with the probability for an n x n Hankel matrix over F_q to be nonsingular. Motivated by this, we give an explicit map from pairs of coprime polynomials to nonsingular Hankel matrices that explains this connection. A basic tool used here is the classical notion of Bezoutian of two polynomials. Moreover, we give simpler and direct proofs of the general formulae for the number of m-tuples of relatively prime polynomials over F_q of given degrees and for the number of n x n Hankel matrices over F_q of a given rank

Affiliated with

Also associated with

No associations

Rating

Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-131027