Relatively prime polynomials and nonsingular Hankel matrices over finite fields
DSpace at IIT Bombay
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Title |
Relatively prime polynomials and nonsingular Hankel matrices over finite fields
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Creator |
GARCIA-ARMAS, M
GHORPADE, SR RAM, S |
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Subject |
Finite field
Relatively prime polynomials Toeplitz matrix Hankel matrix Bezoutian |
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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.
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Publisher |
ACADEMIC PRESS INC ELSEVIER SCIENCE
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Date |
2012-06-26T07:14:02Z
2012-06-26T07:14:02Z 2011 |
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Type |
Article
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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 |
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Language |
English
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