26 research outputs found
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
Geometry of the Wiman Pencil, I: Algebro-Geometric Aspects
In 1981 W.L. Edge discovered and studied a pencil of highly
symmetric genus projective curves with remarkable properties. Edge's work
was based on an 1895 paper of A. Wiman. Both papers were written in the
satisfying style of 19th century algebraic geometry. In this paper and its
sequel [FL], we consider from a more modern, conceptual
perspective, whereby explicit equations are reincarnated as geometric objects.Comment: Minor revisions. Now 49 pages, 4 figures. To appear in European
Journal of Mathematics, special issue in memory of W.L. Edg
Geometry of the Wiman Pencil, I: Algebro-Geometric Aspects
In 1981 W.L. Edge discovered and studied a pencil of highly
symmetric genus projective curves with remarkable properties. Edge's work
was based on an 1895 paper of A. Wiman. Both papers were written in the
satisfying style of 19th century algebraic geometry. In this paper and its
sequel [FL], we consider from a more modern, conceptual
perspective, whereby explicit equations are reincarnated as geometric objects.Comment: Minor revisions. Now 49 pages, 4 figures. To appear in European
Journal of Mathematics, special issue in memory of W.L. Edg
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