Summing Pn(cos θ)/p(n) for certain polynomials p(n)

Chromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...

Note on Certain Orthogonal Polynomials

Factorizations of Certain Bivariate Polynomials

We determine the factorization of Xf(X) − Y g(Y ) over K[X, Y ] for all squarefree additive polynomials f, g ∈ K[X] and all fields K of odd characteristic. This answers a question of Kaloyan Slavov, who needed these factorizations in connection with an algebraic-geometric analogue of the Kakeya problem.

The Zeros of Certain Composite Polynomials

we may obtain various theorems on the relative location of the zeros of A 0(2) and An(z) by the familiar method of first finding such relations for two successive Ak{z) and then iterating the relations n times. This method has already been employed in the study of the zeros of sequence (1.1) for the following three cases: (1) for all k, Pk = 0 and yk is real; 1 (2) for all k, yk~m + l—a limitin...

On certain spaces of lattice diagram polynomials

The aim of this work is to study some lattice diagram polynomials ∆D(X, Y ) as defined in [4] and to extend results of [3]. We recall that MD denotes the space of all partial derivatives of ∆D. In this paper, we want to study the space M i,j(X, Y ) which is the sum of MD spaces where the lattice diagrams D are obtained by removing k cells from a given partition, these cells being in the “shadow...