Record Details

Relatively prime polynomials and nonsingular Hankel matrices over finite fields

DSpace at IIT Bombay

View Archive Info
 
 
Field Value
 
Title Relatively prime polynomials and nonsingular Hankel matrices over finite fields
 
Creator GARCIA-ARMAS, M
GHORPADE, SR
RAM, S
 
Subject Finite field
Relatively prime polynomials
Toeplitz matrix
Hankel matrix
Bezoutian
 
Description 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.
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2012-06-26T07:14:02Z
2012-06-26T07:14:02Z
2011
 
Type Article
 
Identifier JOURNAL OF COMBINATORIAL THEORY SERIES A,118(3)819-828
0097-3165
http://dx.doi.org/10.1016/j.jcta.2010.11.005
http://dspace.library.iitb.ac.in/jspui/handle/100/14107
 
Language English