Beweis einiger Determinantentheoreme von Sylvester

Schrijvers Beweis Von Maders Satz

In der Arbeit von Schrijver [3] wird die folgende Formulierung von Maders Satz aus [2] bewiesen (siehe Satz 1). Wir werden skizzieren wie man aus diesem Satz die Formulierung von Maders Satz über kreuzungsfreie H-Wege (siehe Korollar 2) herleiten kann. Eine Menge P von Wegen in einem Graphen G = (V,E) ist kreuzungsfrei, wenn die Schnittmenge der Eckenmengen zweier unterschiedlicher Wege aus P e...

The Sylvester-Chvatal Theorem

The Sylvester-Gallai theorem asserts that every finite set S of points in two-dimensional Euclidean space includes two points, a and b, such that either there is no other point in S is on the line ab, or the line ab contains all the points in S. V. Chvátal extended the notion of lines to arbitrary metric spaces and made a conjecture that generalizes the Sylvester-Gallai theorem. In the present ...

Sylvester versus Gundelfinger

Let Vn be the SL2-module of binary forms of degree n and let V = V1 ⊕ V3 ⊕ V4. We show that the minimum number of generators of the algebra R = C[V ]2 of polynomial functions on V invariant under the action of SL2 equals 63. This settles a 142-year old question.

Rectangular Corner Cutting Sylvester

This paper presents a way to construct the Sylvester A-resultant matrix for three bi-degree (m; n) polynomials whose exponent set is cut oo by rectangles at the corners. The paper also shows that the determinant of this matrix does give the resultant of the three polynomials.

Sylvester ' S Mathematical Papers