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Random polynomials over a finite field
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G. I. Ivchenko
Published/Copyright:
May 9, 2008
Abstract
We consider monic (with higher coefficient 1) polynomials of fixed degree n over an arbitrary finite field GF(q), where q ≥ 2 is a prime number or a power of a prime number. It is assumed that on the set Fn ={ƒn} of all qn such polynomials the uniform measure is defined which assigns the probability q-n to each polynomial. For an arbitrary polynomial ƒn ∈ Fn, its local structure Kn = K(ƒn) is defined as the set of multiplicities of all irreducible factors in the canonical decomposition of ƒn, and various structural characteristics of a polynomial (its exact and asymptotic as n → ∞ distributions) which are functionals of Kn are studied. Directions of possible further research are suggested.
Received: 2007-02-22
Published Online: 2008-05-09
Published in Print: 2008-March
© de Gruyter 2008
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Articles in the same Issue
- Random polynomials over a finite field
- Random permutations with cycle lengths in a given finite set
- The Kloss convergence principle for products of random variables with values in a compact group and distributions determined by a Markov chain
- On enumeration of labelled connected graphs by the number of cutpoints
- Skew Laurent series rings and the maximum condition on right annihilators
- A block algorithm of Lanczos type for solving sparse systems of linear equations
- On complexity of the anti-unification problem
- Classification of indecomposable Abelian (v, 5)-groups
