Name
Abstract | ||
|---|---|---|
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 nxn 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 nxn Hankel matrices over F"q of a given rank. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jcta.2010.11.005 | The Journal of Chemical Thermodynamics |
Keywords | Field | DocType |
explicit map,bezoutian,hankel matrix,relatively prime polynomials,coprime polynomial,direct proof,classical notion,finite field f,nxn hankel matrix,bezoutian.,finite field,prime polynomial,toeplitz matrix,. finite field,nonsingular hankel matrix,basic tool,general formula | Wilson polynomials,Combinatorics,Finite field,Orthogonal polynomials,Classical orthogonal polynomials,Matrix (mathematics),Discrete orthogonal polynomials,Hankel matrix,Coprime integers,Mathematics | Journal |
Volume | Issue | ISSN |
118 | 3 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
3 | 0.57 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mario García-Armas | 1 | 3 | 0.57 |
| Sudhir R. Ghorpade | 2 | 80 | 12.16 |
| Samrith Ram | 3 | 20 | 3.52 |