Related papers: Division properties of commuting polynomials
Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a…
We study an infinite class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. This generalizes a sequence of sparse polynomials which arises in a natural way as graph theoretic…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
Some Dirichlet-like functions, attached to a pair (periodic function, polynomial) are introduced and studied. These functions generalize the standard Dirichlet L-functions of Dirichlet characters. They have similar properties, being…
In this paper we deal with composite rational functions having zeros and poles forming consecutive elements of an arithmetic progression. We also correct a result published earlier related to composite rational functions having a fixed…
Graph polynomials are polynomials assigned to graphs. Interestingly, they also arise in many areas outside graph theory as well. Many properties of graph polynomials have been widely studied. In this paper, we survey some results on the…
It is known that the Ehrhart polynomials of cross-polytopes, as well as of pyramids over them, have positive coefficients. We give a combinatorial proof of this fact by showing that a scaled version of the Ehrhart polynomials are generating…
We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…
In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…
In this paper we find coomon eigenfunctions of commuting differential operators of rank 2 with polynomial coefficients in some partial cases.
We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…
Elementary properties of the Koornwinder-Macdonald multivariable Askey-Wilson polynomials are discussed. Studied are the orthogonality, the difference equations, the recurrence relations, and the orthonormalization constants for these…
This paper describes how many known graph polynomials arise from the coefficients of chromatic symmetric function expansions in different bases, and studies a new polynomial arising by expanding over a basis given by chromatic symmetric…
We consider polynomials with integer coefficients and discuss their factorization properties in Z[[x]], the ring of formal power series over Z. We treat polynomials of arbitrary degree and give sufficient conditions for their reducibility…
In this expositional paper, we discuss commutative algebra -- a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases…
A partition polynomial is a refinement of the partition number p(n) whose coefficients count some special partition statistic. Just as partition numbers have useful asymptotics so do partition polynomials. In fact, their asymptotics…
The chromatic polynomials are studied by several authors and have important applications in different frameworks, specially, in graph theory and enumerative combinatorics. The aim of this work is to establish some properties of the…
We investigate a family of permutation polynomials of finite fields of characteristic 2. Through a connection between permutation polynomials and quadratic forms, a general treatment is presented to characterize these permutation…