Dave Futer
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Registered User
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Apr 25 |
accepted | Diagrammatic proof of unique prime decomposition of knots |
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Apr 24 |
comment |
Diagrammatic proof of unique prime decomposition of knots Ryan, that's a good point. In fact, it brings up the grey and amorphous boundary of the "diagrammatic" concept. For instance, take Menasco's proof that prime decompositions of alternating knots must be visible in the diagram. That argument is diagrammatic in flavor, but cut-and-paste topology (of the kind that Daniel seems to want to rule out) is also present. So is this in or out? |
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Apr 24 |
revised |
Diagrammatic proof of unique prime decomposition of knots added 219 characters in body |
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Apr 24 |
answered | Diagrammatic proof of unique prime decomposition of knots |
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Apr 24 |
revised |
Untwisting Heegaard diagrams added 9 characters in body; added 33 characters in body; deleted 26 characters in body |
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Apr 24 |
comment |
Untwisting Heegaard diagrams Scott: I take your point, and mostly agree with it. In fact, I would argue that the most interesting splittings are of distance 2. (Either less than 2 or more than 2 provides a lot of additional information.) But by the above update, splittings with rectangles must be weakly reducible -- at least in high genus, and probably in every genus. |
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Apr 24 |
revised |
Untwisting Heegaard diagrams added 1019 characters in body |
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Apr 23 |
accepted | Untwisting Heegaard diagrams |
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Apr 23 |
answered | Untwisting Heegaard diagrams |
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Nov 28 |
comment |
Generic words of given weight Thanks Fedja - if posting here is difficult, or if it's something that would be of limited interest to the MO community, feel free to just contact me directly. My email address is easy to google for. |
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Nov 27 |
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Generic words of given weight Thank you -- please do add an explanation assuming the basics. I will try to backfill the basics as needed. |
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Nov 27 |
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Generic words of given weight Also, one phrase that I cannot parse at all is "the mountain pass in the circle method". Thanks for answering my stupid questions! |
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Nov 27 |
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Generic words of given weight Thank you, Fedja! As I'm quite ignorant of this area of math, it's somewhat opaque to me why these particular generating functions arise. Perhaps you can point me to a reference that explains the "cookbook" for this type of counting question? |
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Nov 27 |
comment |
Generic words of given weight Nope - all the letters in the alphabet are distinct. But we are allowed to use each one many times. I'm thinking of them as, eg, generators of a group (except we're not simplifying the word at all). |
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Nov 26 |
asked | Generic words of given weight |
