Related papers: A note in algebras with Laurent polynomial identit…
In this article we shows some results about algebra with the group of units having special polynomial identity.
Let $KG$ be the group algebra of a torsion group $G$ over a field $K$. We show that if the units of $KG$ satisfy a Laurent polynomial identity which is not satisfied by the units of the relative free algebra $K[\alpha,\beta :…
Let A be an algebra whose group of units U(A) satisfies a Laurent polynomial identity (LPI). We establish conditions on these polynomials in such a way that nil-generated algebras and group algebras with torsion groups over infinite fields…
We establish an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients.
A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes---quite unexpectedly---it does. We suggest a unified treatment of this phenomenon, which covers a large class of…
This is a slightly edited version of my talk on Mathematische Arbeitstagung 2011, Bonn. I present a result relating noncommutative Laurent polynomials with algebraic functions, and show examples of integrability and Laurent phenomenon for…
In this paper we obtain several new identities for Bernoulli and Euler polynomials; some of them extend Miki's and Matiyasevich's identities. Our new method involves differences and derivatives of polynomials.
In a cluster algebra, a subset of initial cluster variables can be specialised in such a way that all elements of the resulting algebra become polynomial in the remaining variables.
In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have…
We establish a weak form of Ennola's conjecture. We achieve this by showing that two main assumptions Louboutin made in his previous work hold true. These assumptions are about Laurent polynomials over the rationals, and we prove them by…
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
In this papier, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities.
We provide new approaches to prove identities for the modified Macdonald polynomials via their LLT expansions. As an application, we prove a conjecture of Haglund concerning the multi-$t$-Macdonald polynomials of two rows.
In a field of Laurent series, we construct a subring which has a module structure over a Weyl algebra. Identities of Bernoulli numbers and polynomials are obtained from these algebraic structures.
In the paper we provide some polynomial identities for finite-dimensional algebras. A list of well known single polynomial identities is exposed and the classification of all $2$-dimensional algebras with respect to these identities is…
In this paper, we study some properties of associated sequaences in umbral calculus. From these properties, we derive new and interesting identities of several kinds of polynomials.
In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.
The paper [GLZ] "L-functions of Carlitz modules, resultantal varieties and rooted binary trees" is devoted to a description of some resultantal varieties related to L-functions of Carlitz modules. It contains a conjecture that some of these…
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
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.