Related papers: A Goldbach theorem for Laurent polynomials with po…

In this article we study asymptotic behavior of the probability that a random monic polynomial with integer coefficients is irreducible over the integers. We consider the cases where the coefficients grow together with the degree of the…

We prove a positivity result in (T-)equivariant quantum cohomology of the homogeneous space G/P, generalizing Graham's positivity in equivariant cohomology.

We generalize a semi-norm for the Alexander polynomial of a connected, compact, oriented 3-manifold on its first cohomology group to a semi-norm for an arbitrary Laurent polynomial f on the dual vector space to the space of exponents of f.…

We generalize the Wiener-Hopf factorization of Laurent series to more general commutative coefficient rings, and we give explicit formulas for the decomposition. We emphasize the algebraic nature of this factorization.

Goulden-Rattan polynomials give the exact value of the subdominant part of the normalized characters of the symmetric groups in terms of certain quantities ($C_i$) which describe the macroscopic shape of the Young diagram. The…

It is shown that some q-analogues of the Fibonacci and Lucas polynomials lead to q-analogues of the Chebyshev polynomials which retain most of their elementary properties.

Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.

The linearization coefficients for a set of orthogonal polynomials are given explicitly as a weighted sum of combinatorial objects. Positivity theorems of Askey and Szwarc are corollaries of these expansions.

We introduce and discuss a variant of Schanuel conjecture in the framework of the Carlitz exponential function over Tate algebras and allied functions. Another purpose of the present paper is to widen the horizons of possible investigations…

In this article, we give an account of some recent irreducibility testing criteria for polynomials having integer coefficients over the field of rational numbers.

In this paper, we prove the K- and L-theoretical Isomorphism Conjecture for Baumslag-Solitar groups with coefficients in an additive category.

We prove a conjecture of Kontsevich regarding the solutions of rank two recursion relations for non-commutative variables which, in the commutative case, reduce to rank two cluster algebras of affine type. The conjecture states that…

We develop a polynomial analogue of Meinardus' Thoerem for bivariate Euler products and apply it to the study of complex multiplicatively weighted partitions.

We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of…

It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties similar to the Riemann {\zeta} function. The construction was generalized by Matsui et al. to a larger family of reflexive polytopes coming from…

We prove a recent conjecture by Ulas on reducible polynomial substitutions.

In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane.

In this work we use the number classification in families of the form 6n+1, and 6n+5 with n integer (Such families contain all odd prime numbers greater than 3 and other compound numbers related with primes). We will use this kind of…

In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.

In this paper we give a matrix version of Handelman's Positivstellensatz [1], representing polynomial matrices which are positive definite on convex, compact polyhedra. Moreover, we propose also a procedure to find such a representation. As…