# Günter Rote

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bio website location DE age member for 1 year, 3 months seen Oct 22 '13 at 19:18 profile views 281

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 Jan20 awarded Yearling Oct22 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.) Oct11 awarded Necromancer Oct11 answered Tiling A Rectangle With A Hint of Magic Oct10 revised How many vertices/edges/faces at most for a convex polyhedron that tiles space? added the original reference of the figure Oct10 suggested suggested edit on How many vertices/edges/faces at most for a convex polyhedron that tiles space? Oct8 revised The Cayley Menger Theorem and integer matrices with row sum 2 small clarification Oct8 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). Oct7 answered Vertices of a Polytope Sep18 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"? Jun25 awarded Revival Jun25 awarded Excavator Apr28 comment What is the expected value for this The exponent would not change. For example, take random points in a circular disk. Fit a triangle in the disk. A constant fraction of the n points falls inside the triangle (w.h.p.), and thus you get at least $c′n^{1/3}$ points in convex position; similarly, an ellipse (affine image of a disk) fits into any triangle, showing the other direction of the inequality. Any two convex shapes are related like this (after affine transformation). Apr28 revised The Cayley Menger Theorem and integer matrices with row sum 2 corrected info about the sign Apr28 comment The Cayley Menger Theorem and integer matrices with row sum 2 Yes, it is. I have updated my answer. Apr26 answered The Cayley Menger Theorem and integer matrices with row sum 2 Apr26 comment The Cayley Menger Theorem and integer matrices with row sum 2 I wonder how a matrix with positive entries can have trace 0? Mar21 revised functions satisfying “one-one iff onto” typos, grammar Mar6 comment long enough interval of integers to solve a simultaneous congruence @Noam. Clarification: I was not puzzled because I did not see that the product has "distinct" exponents, after expanding the product and before collecting terms with the same exponent. But why is this fact needed? Mar6 answered All possible linear combinations of positive half-integers with coefficients +/- 1