DSpace at IIT Bombay >
IITB Publications >
Please use this identifier to cite or link to this item:
|Title: ||Relatively prime polynomials and nonsingular Hankel matrices over finite fields|
|Authors: ||GARCIA-ARMAS, M|
|Issue Date: ||2011|
|Publisher: ||ACADEMIC PRESS INC ELSEVIER SCIENCE|
|Citation: ||JOURNAL OF COMBINATORIAL THEORY SERIES A,118(3)819-828|
|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 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. (C) 2010 Elsevier Inc. All rights reserved.|
|Appears in Collections:||Article|
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.