Determinants whose elements have equal norm

Determinants Whose Elements Have Equal Norm1

Hence A, B, C equal A', B', C in some order. Each of the 6 orders leads immediately to the proportionality of two rows or columns. The above theorem, in its specialization to minors of Vandermonde determinants composed of gth roots of unity in R*, was used in [l] for the proof of a theorem on power series without terms whose subscript belongs to one of 3 residue classes modulo an arbitrary inte...

Polygons Whose Vertex Triangles Have Equal Area

On Counterexamples to a Conjecture of Wills and Ehrhart Polynomials whose Roots have Equal Real Parts

As a discrete analog to Minkowski’s theorem on convex bodies, Wills conjectured that the Ehrhart coefficients of a 0-symmetric lattice polytope with exactly one interior lattice point are maximized by those of the cube of side length two. We discuss several counterexamples to this conjecture and, on the positive side, we identify a family of lattice polytopes that fulfill the claimed inequaliti...

Classes of Finite Equal Norm Parseval Frames

Finite equal norm Parseval frames are a fundamental tool in applications of Hilbert space frame theory. We will derive classes of finite equal norm Parseval frames for use in applications as well as reviewing the status of the currently known classes.

On the size of sets whose elements have perfect power n - shifted products

We show that the size of sets A having the property that with some non-zero integer n, a1a2 + n is a perfect power for any distinct a1, a2 ∈ A, cannot be bounded by an absolute constant. We give a much more precise statement as well, showing that such a set A can be relatively large. We further prove that under the abcconjecture a bound for the size of A depending on n can already be given. Ext...