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Jim Conant's user avatar
Jim Conant's user avatar
Jim Conant's user avatar
Jim Conant
  • Member for 14 years, 3 months
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Can we cover the unit square by these rectangles?
It's a little disappointing to realize that the (1+1/m)^2 bounds are really just a fancy way of saying somebody succeeded in fitting $m-1$ rectangles.
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Can we cover the unit square by these rectangles?
Well I guess Ed Wynn's computations improve the (501/500)^2 bound by quite a stretch.
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Geometric (smooth) Rubik's cube
What happens at $S^2\cap H$? Does that part move?
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Consequences of lack of rigour
@YCor, I believe the OP wants all 4 criteria to hold, so most wrong theorems wouldn't apply.
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Borromean braids
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Is there any solution that currently exists for the graph automorphism problem in the general case?
There's an obvious brute force solution for finite graphs. Are you talking about infinite graphs?
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Statistics for mathematicians
I like this answer, just wish it weren't so polemical.
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Are there knots that can be distinguished by the Alexander-Conway polynomial, but not the Alexander polynomial?
I want to point out that although the Alexander-Conway polynomial cannot distinguish a knot from its mirror image, it can detect certain kinds of chirality. In fact, I made a conjecture many years ago that I wish someone would solve. Any amphicheiral knot has conway polynomial that splits as $f(z)f(-z)$ with coefficients taken modulo $4$. See arxiv.org/pdf/1608.04453.pdf
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Intuition behind Alexander duality
@MatthewKvalheim: yes! fixed.
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Applications of E8 manifold
I wonder whether any non-smoothable manifolds have any reasonably direct applications outside pure mathematics. Interesting question.
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