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visits member for 1 year, 9 months
seen Oct 22 '13 at 19:18

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 suggested 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
Jun
25
awarded  Excavator
Apr
28
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).
Apr
28
revised The Cayley Menger Theorem and integer matrices with row sum 2
corrected info about the sign
Apr
28
comment The Cayley Menger Theorem and integer matrices with row sum 2
Yes, it is. I have updated my answer.
Apr
26
answered The Cayley Menger Theorem and integer matrices with row sum 2
Apr
26
comment The Cayley Menger Theorem and integer matrices with row sum 2
I wonder how a matrix with positive entries can have trace 0?
Mar
21
revised functions satisfying “one-one iff onto”
typos, grammar
Mar
6
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?
Mar
6
answered All possible linear combinations of positive half-integers with coefficients +/- 1