Rüdinger, Andreas

Asymptotic Distribution of Form of Polyhedra ★★

Author(s): Rüdinger

\begin{problem} Consider the set of all topologically inequivalent polyhedra with $k$ edges. Define a form parameter for a polyhedron as $\beta:= v/(k+2)$ where $v$ is the number of vertices. What is the distribution of $\beta$ for $k \to \infty$? \end{problem}

Keywords: polyhedral graphs, distribution

Criterion for boundedness of power series

Author(s): Rüdinger

\begin{question} Give a necessary and sufficient criterion for the sequence $(a_n)$ so that the power series $\sum_{n=0}^{\infty} a_n x^n$ is bounded for all $x \in \mathbb{R}$. \end{question}

Keywords: boundedness; power series; real analysis

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