Günter Rote
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 Jan 20 awarded Yearling Jul 31 awarded Necromancer Jan 20 awarded Yearling Dec 11 comment “Circular” domination in ${\mathbb R}^4$ Why is the first reduction from $S$ to $S'$ true? For example, when $(5,5,5,1),(1,1,1,5)\in S$, then there must exist a vector that dominates $(5,5,5,5)$. But $(5,5,5,5)$ cannot be built as the elementwise maximum from two of the twelve "two-coordinate" versions $(5,5,0,0),(5,0,5,0),\ldots,(0,0,1,5)$. Nov 26 comment A problem on chains of squares — can one find an easy combinatorial proof? A) What is the well-known solution that uses Brouwer's fixed-point theorem? B) The discrete problem has definitely easy direct proofs, just by specializing the polygonal Jordan curve theorem. C) If the two paths don't cross, one can extend them to a crossing-free drawing of the (non-planar) complete bipartite graph $K_{3,3}$ by adding two new vertices and some curves outside the square. But I guess this does not count, as non-planarity of $K_{3,3}$ is based on Euler's polyhedral formula, and that in turn depends on the Jordan curve theorem, it seems. Nov 26 comment Powers of orthogonal matrices is closed @Sebastian, What do you mean, "any real matrix", for which matrix? Was my argument not short enough? Nov 26 revised Simplifying triangulations of 3-manifolds fixed grammar and spelling Nov 26 answered Powers of orthogonal matrices is closed Nov 26 suggested approved edit on Simplifying triangulations of 3-manifolds Jan 20 awarded Yearling Oct 22 comment Tiling a rectangle with weighted cells (min-max problem) What precisely do you mean by "sparse"? A constant number of entries in each row and column? At most $m+n$ entries in total? Or why would the total number of entries not appear in the runtime? (And edit the problem rather than posting an answer) (And the upper bound $a,b<1$ seems to be irrelevant.) Oct 11 awarded Necromancer Oct 11 answered Tiling A Rectangle With A Hint of Magic Oct 10 revised How many vertices/edges/faces at most for a convex polyhedron that tiles space? added the original reference of the figure Oct 10 suggested approved edit on How many vertices/edges/faces at most for a convex polyhedron that tiles space? Oct 8 revised The Cayley Menger Theorem and integer matrices with row sum 2 small clarification Oct 8 comment Vertices of a Polytope Indeed, fullerenes are a good example. Almost all of the surface is a hexagonal lattice, and there you can simultaneously cut away vertices as long as their minimum distance is 2. Thus, you can cut away half of the vertices (almost; staying away from the pentagons). Oct 7 answered Vertices of a Polytope Sep 18 comment Is there a 3d equivalent of this picture? 1. It should be pointed out that the density does not increase indefinitely inside the "black spot" but there is some minimum distance (if the points were really generated as indicated in the text) 2. Would you tolerate, for example (in the planar example) occasional vertices with 5 or 7 incident triangles, or should it be "completely regular"? Jun 25 awarded Revival