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Degree distribution of the greatest common divisor of polynomials over 𝔽 q
Author(s) -
Gao Zhicheng,
Panario Daniel
Publication year - 2006
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20093
Subject(s) - mathematics , degree (music) , greatest common divisor , poisson distribution , finite field , divisor (algebraic geometry) , distribution (mathematics) , combinatorics , degree distribution , irreducible polynomial , discrete mathematics , statistics , polynomial , mathematical analysis , physics , matrix polynomial , acoustics , complex network
We study the degree distribution of the greatest common divisor of two or more random polynomials over a finite field q . We provide estimates for several parameters like number of distinct common irreducible factors, number of irreducible factors counting repetitions, and total degree of the gcd of two or more polynomials. We show that the limiting distribution of a random variable counting the total degree of the gcd is geometric and that the distributions of random variables counting the number of common factors (with and without repetitions) are very close to Poisson distributions when q is large. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006