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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/100/13836

Title: Relatively prime polynomials and nonsingular Hankel matrices over finite fields
Authors: GARCIA-ARMAS, M
GHORPADE, SR
RAM, S
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.
URI: http://dx.doi.org/10.1016/j.jcta.2010.11.005
http://dspace.library.iitb.ac.in/jspui/handle/100/13836
ISSN: 0097-3165
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