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Rüdinger, Andreas
Asymptotic Distribution of Form of Polyhedra ★★
Author(s): Rüdinger
Problem Consider the set of all topologically inequivalent polyhedra with
edges. Define a form parameter for a polyhedron as
where
is the number of vertices. What is the distribution of
for
?
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ \beta:= v/(k+2) $](/files/tex/85e33eb70cd1ead9d25ddd845e229cfa8d4c937a.png)
![$ v $](/files/tex/96cbd9a16c6a5eab03815b093b08f3b2db614e9a.png)
![$ \beta $](/files/tex/624e933e0823c4484fba477a090a0dfc8aa2fc56.png)
![$ k \to \infty $](/files/tex/f17af0206807b43e4ef529e6e21924cfde801683.png)
Keywords: polyhedral graphs, distribution
Criterion for boundedness of power series ★
Author(s): Rüdinger
Question Give a necessary and sufficient criterion for the sequence
so that the power series
is bounded for all
.
![$ (a_n) $](/files/tex/0343ff13b16e6d39031bcb59a0d31a300a582fd0.png)
![$ \sum_{n=0}^{\infty} a_n x^n $](/files/tex/722a4892fa6950b75b1122e5f22a3459d58ec674.png)
![$ x \in \mathbb{R} $](/files/tex/e3182ddcb88f01afefb8cee99a8319c4deb28f83.png)
Keywords: boundedness; power series; real analysis
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