16 research outputs found
The invariants of the binary nonic
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 of degrees
On the self-convolution of generalized Fibonacci numbers
We focus on a family of equalities pioneered by Zhang and generalized by Zao
and Wang and hence by Mansour which involves self convolution of generalized
Fibonacci numbers. We show that all these formulas are nicely stated in only
one equation involving a bivariate ordinary generating function and we give
also a formula for the coefficients appearing in that context. As a
consequence, we give the general forms for the equalities of Zhang, Zao-Wang
and Mansour
The invariants of the binary decimic
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
Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method
2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.An analogue of the symbolic method of classical invariant theory for a representation and manipulation of the elements of the kernel of Weitzenböck derivations is developed
SL2-modules of small homological dimension
Let Vn be the SL2-module of binary forms of degree n and let V = Vn1+...+Vnp
. We consider the algebra R of polynomial functions on V invariant under the
action of SL2. The measure of the intricacy of these algebras is the length of
their chains of syzygies, called homological dimension hdR. Popov gave in 1983
a classification of the cases in which hdR <=10 for a single binary form (p =
1) or hdR 1). We extend
Popov's result and determine for p = 1 the cases with hdR 1
those with hdR <= 15. In these cases we give a set of homogeneous parameters
and a set of generators for the algebra R