相关论文: A note on polynomials for character degrees
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials
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 1961, Solomon gave upper and lower bounds for the sum of all the entries in the character table of a finite group in terms of elementary properties of the group. In a different direction, we consider the ratio of the character table sum…
We present various constructions of sequences of polynomials satisfying the Binomial Theorem in finite characteristic based on the theory of additive polynomials. Various actions on these constructions are also presented. It is an open…
We study identities of finite dimensional algebras over a field of characteristic zero, graded by an arbitrary groupoid $\Gamma$. First we prove that its graded colength has a polynomially bounded growth. For any graded simple algebra $A$…
A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, allowing a unified treatment of a large body of polynomial…
We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of a character in terms of its Lusztig's label and in terms of…
In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series…
We give new identities for some symmetric polynomials. As applications of these identities, we obtain some formulas for a higher order analogue of Fibonacci and Lucas numbers.
The theory of character sheaves on a reductive group is extended to a class of varieties which includes the strata of the De Concini-Procesi completion of an adjoint group.
We present an extension theorem for a separately holomorphic function which is polynomial/rational in some variables.
I demonstrate how certain identities for Macdonald's polynomials established by Garsia, Haiman and Tesler, together with the conjecture of Hausel, Letellier and Villegas imply explicit relations between mixed Hodge polynomials of different…
We prove the existence of complex polynomials $p(z)$ of degree $n$ and $q(z)$ of degree $m<n$ such that the harmonic polynomial $ p(z) + \overline{q(z)}$ has at least $\lceil n \sqrt{m} \rceil$ many zeros. This provides an array of new…
A method is described which allows to evaluate efficiently a polynomial in a (possibly trivial) extension of the finite field of its coefficients. Its complexity is shown to be lower than that of standard techniques when the degree of the…
In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.
This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.
In this paper we obtained the formula for the number of irreducible polynomials with degree $n$ over finite fields of characteristic two with given trace and subtrace. This formula is a generalization of the result of Cattell et al.(2003)…
The finite-degree Zariski (Z-) closure is a classical algebraic object, that has found a key place in several applications of the polynomial method in combinatorics. In this work, we characterize the finite-degree Z-closures of a subclass…
We prove certain polynomial relations between the values of complex irreducible characters of general finite symmetric groups. We use it to find some sets of conjugacy classes such that no finite symmetric group has a complex irreducible…