Counting reducible and singular bivariate polynomials

Counting Reducible Matrices, Polynomials, and Surface and Free Group Automorphisms

A. We give upper bounds on the numbers of various classes of polynomials reducible over Z and over Z/pZ, and on the number of matrices in SL(n),GL(n) and Sp(2n) with reducible characteristic polynomials, and on polynomials with non-generic Galois groups. We use our result to show that a random (in the appropriate sense) element of the mapping class group of a closed surface is pseudo-Ano...

Galois Theory and Reducible Polynomials

This paper presents works on reducible polynomials in Galois theory. It gives a fundamental theorem about the Galois ideals associated with a product of groups. These results are used for the practical determination of Galois groups of polynomials of degrees up to 7. : : :). The following tools are used: resolvents (relative or absolute), p-adic methods, Grr obner bases or block systems. In gen...

On Counting Polynomials of Some Nanostructures

The Omega polynomial(x) was recently proposed by Diudea, based on the length of strips in given graph G. The Sadhana polynomial has been defined to evaluate the Sadhana index of a molecular graph. The PI polynomial is another molecular descriptor. In this paper we compute these three polynomials for some infinite classes of nanostructures.

Reducible cubic CNS polynomials

The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational integers to elements of residue class rings of polynomial rings. Generators of canonical number systems are CNS polynomials which are known in the linear and quadratic cases, but whose complete description is still open. In the present note reducible CNS polynomials are tr...

Counting Reducible, Powerful, and Relatively Irreducible Multivariate Polynomials over Finite Fields