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qaaa We provide a simple proof for the equality between the normalized volume of a convex polytope with m vertices and the mixed volume of m simplices and thus show the seemingly restrictive problem of computing the mixed volume of simplices is still at least as hard as computing volumes of...
Using deformation theory, we answer two questions of Shioda concerning the infinitesimal structure of the moduli space of integral sections in the Mordell–Weil group.
It is known that every finite group can be represented as the full group of automorphisms of a suitable compact origami. In this paper, we provide a short argument to note that the same holds for any countable group by considering origamis on the Loch Ness monster.
Combinatorics is full of examples of real-rooted polynomials. Suppose one has a sequence of real-rooted polynomials, and then wants consecutive pairs to have interlacing roots (on the real line). The method of proving the real-rootedness sometimes does not prove the interlacing property. In this...
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