<p style='text-indent:20px;'>We give a complete classification of Dembowski-Ostrom polynomials from the composition Dickson arbitrary kind and monomials over finite fields. Moreover, by using variant Weil bound for number points affine algebraic curves fields, we discuss planarity obtained polynomials.</p>

The main goal of this paper is to characterize limit key polynomials for a valuation ν on K [ x ] . We consider the set Ψ α degree p be exponent characteristic Our first result ( Theorem 1.1 ) that if F polynomial , then r some ∈ N Moreover, in 1.2 we show there exist Q and such -expansion only has terms which are powers

In [3], H. Belbachir and F. Bencherif generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. They prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations. [7], Mario Catalani define generalized bivariate polynomials, from which specifying initial conditi...

Multiple orthogonal polynomials are polynomials in one variable that satisfy orthogonality conditions with respect to several measures. I will briefly give some general properties of these polynomials (recurrence relation, zeros, etc.). These polynomials have recently appeared in many applications, such as number theory, random matrices, non-intersecting random paths, integrable systems, etc. I...

We study polynomials which satisfy the same recurrence relation as the Szegő polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal polynomials that follow from these Szegő polynomials are also considered. With positive values for the reflection coefficients, zeros of the Szegő polynomials, para-orthogonal ...

We study the Hamming distance from polynomials to classes of polynomials that share certain properties of irreducible polynomials. The results give insight into whether or not irreducible polynomials can be effectively modeled by these more general classes of polynomials. For example, we prove that the number of degree n polynomials of Hamming distance one from a randomly chosen set of b2n/nc o...

We express a weighted generalization of the Delannoy numbers in terms of shifted Jacobi polynomials. A specialization of our formulas extends a relation between the central Delannoy numbers and Legendre polynomials, observed over 50 years ago [12, 17, 19], to all Delannoy numbers and certain Jacobi polynomials. Another specialization provides a weighted lattice path enumeration model for shifte...