Related papers: Invariants of polynomials and binary forms

We consider the algebra of invariants of binary forms of degree 10 with complex coefficients, construct a system of parameters with degrees 2, 4, 6, 6, 8, 9, 10, 14 and find the 106 basic invariants.

We consider the algebra of invariants of binary forms of degree 9 with complex coefficients, find the 92 basic invariants, give an explicit system of parameters and show the existence of four more systems of parameters with different sets…

Using the methods of classical invariant theory a general approach to finding of identities for Bernulli, Euler and Hermite polynomials is proposed.

We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.

We present an algebraic theory of orthogonal polynomials in several variables that includes classical orthogonal polynomials as a special case. Our bottom line is a straightforward connection between apolarity of binary forms and the inner…

In these notes we investigate the rings of real polynomials in four variables, which are invariant under the action of the reflectiongroups [3,4,3] and [3,3,5]. It is well known that they are rationally generated in degree 2,6,8,12 and…

Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.

We calculate the degree of the algebra of covariants $\mathcal{C}_d$ for binary $d$-form. Also, for the degree we obtain its integral representation and asymptotic behavior.

Here we develop a technique of computing the invariants of $n-$ary forms and systems of forms using the discriminants of corresponding multilinear forms built of their partial derivatives, which should be cosidered as analogues of classical…

We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the…

In this paper, for n a positve integer, we compute the number of n degree representations for a dihedral group G of order 2m, m \geq 3 and the dimensions of the corresponding spaces of G invariant bilinear forms over a complex field C. We…

We introduce a system of invariants of isotopy classes of Morse polynomials ${\mathbb R}^2 \to {\mathbb R}^1$, prove its completeness for polynomials of degrees $\leq 4$, calculate all 71 possible values of these invariants for the case of…

We introduce a multivariate analogue of Bernoulli polynomials and give their fundamental properties: difference and differential relations, symmetry, explicit formula, inversion formula, multiplication theorem, and binomial type formula.…

We give an explicit upper bound for the number of equivalence classes of binary forms with rational integral coefficients of given degree and given discriminant, and with given splitting field. Further, we give an explicit upper bound for…

We consider the degrees of the elements of a homogeneous system of parameters for the ring of invariants of a binary form, give a divisibility condition, and a complete classification for forms of degree at most 8.

Explicit formulas for computation of the Poincar\'e series for the algebras of joint $SL_2$-invariants and covariants of $n$ linear forms in terms of Narayana polynomials are found. Also, for these algebras we calculate the degrees and…

We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.

A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them…

For each 3-dimensional non-Lie Leibniz algebra over the complex numbers, we describe the algebra of polynomial invariants and determine its group of automorphisms. As a consequence, we establish that any two non-nilpotent 3-dimensional…

In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.