Journal of Integer Sequences, Vol. 17 (2014), Article 14.2.4

On the Number of Polynomials of Bounded Height that Satisfy the Dumas Criterion

Randell Heyman
Department of Computing
Macquarie University
Sydney, NSW 2109


We study integer coefficient polynomials of fixed degree and maximum height H that are irreducible by the Dumas criterion. We call such polynomials Dumas polynomials. We derive upper bounds on the number of Dumas polynomials as H → ∞. We also show that, for a fixed degree, the density of Dumas polynomials in the set of all irreducible integer coefficient polynomials is strictly less than 1.

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Received June 3 2013; revised version received December 12 2013; Published in Journal of Integer Sequences, January 4 2014.

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