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The classical 1966 theorem of Tverberg with its numerous variations was and still is a motivating force behind many important developments in convex and computational geometry as well as the testing ground for methods from equivariant algebraic topology. In 2018, Barany and Soberon presented a new variation, the Tverberg plus minus theorem. In this paper, we give a new proof of the Tverberg plus minus theorem, by using a projective transformation. The same tool allows us to derive plus minus analogues of all known affine Tverberg type results. In particular, we prove a plus minus analogue of the optimal colored Tverberg theorem.
Recent theoretical advances applied to metamaterials have opened new avenues to design a coating that hides objects from electromagnetic radiation and even the sight. Here, we propose a new design of cloaking devices that creates perfect invisibility
Let $T(d,r) = (r-1)(d+1)+1$ be the parameter in Tverbergs theorem, and call a partition $mathcal I$ of ${1,2,ldots,T(d,r)}$ into $r$ parts a Tverberg type. We say that $mathcal I$ occurs in an ordered point sequence $P$ if $P$ contains a subsequence
We show that for any compact convex set $K$ in $mathbb{R}^d$ and any finite family $mathcal{F}$ of convex sets in $mathbb{R}^d$, if the intersection of every sufficiently small subfamily of $mathcal{F}$ contains an isometric copy of $K$ of volume $1$
We study the validity of a partition property known as weak indivisibility for the integer and the rational Urysohn metric spaces. We also compare weak indivisiblity to another partition property, called age-indivisibility, and provide an example of
In basketball and hockey, state-of-the-art player value statistics are often variants of Adjusted Plus-Minus (APM). But APM hasnt had the same impact in soccer, since soccer games are low scoring with a low number of substitutions. In soccer, perhaps