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Search: MSC category 52C99 ( None of the above, but in this section )

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1. CMB 2010 (vol 53 pp. 394)

Averkov, Gennadiy
On Nearly Equilateral Simplices and Nearly l∞ Spaces
By $\textrm{d}(X,Y)$ we denote the (multiplicative) Banach--Mazur distance between two normed spaces $X$ and $Y.$ Let $X$ be an $n$-dimensional normed space with $\textrm{d}(X,\ell_\infty^n) \le 2,$ where $\ell_\infty^n$ stands for $\mathbb{R}^n$ endowed with the norm $\|(x_1,\dots,x_n)\|_\infty := \max \{|x_1|,\dots, |x_n| \}.$ Then every metric space $(S,\rho)$ of cardinality $n+1$ with norm $\rho$ satisfying the condition $\max D / \min D \le 2/ \textrm{d}(X,\ell_\infty^n)$ for $D:=\{ \rho(a,b) : a, b \in S, \ a \ne b\}$ can be isometrically embedded into $X.$

Categories:52A21, 51F99, 52C99

2. CMB 2009 (vol 52 pp. 327)

Berman, Leah Wrenn; Bokowski, Jürgen; Grünbaum, Branko; Pisanski, Toma\v{z}
Geometric ``Floral'' Configurations
With an increase in size, configurations of points and lines in the plane usually become complicated and hard to analyze. The ``floral'' configurations we are introducing here represent a new type that makes accessible and visually intelligible even configurations of considerable size. This is achieved by combining a large degree of symmetry with a hierarchical construction. Depending on the details of the interdependence of these aspects, there are several subtypes that are described and investigated.

Categories:52C30, 52C99

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