Timeline for How do we know there are no more Deligne–Mostow/Thurston lattices?
Current License: CC BY-SA 4.0
9 events
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| Mar 9, 2023 at 20:53 | answer | added | Peter Taylor | timeline score: 6 | |
| Mar 9, 2023 at 9:13 | comment | added | Peter Taylor |
Ah, that was my stupidity. I saw that in the condition of Theorem 0.2, made a note of it, and then forgot about it when writing the code. The other thing which is missing is a gcd filter to remove e.g. 3 3 3 3 3 3 for $q=9$. I've also optimised the checking and it can do up to 300 well within the 1 minute restriction of tio.run. On a desktop it takes a bit over a quarter of an hour to run up to 1000.
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| Mar 9, 2023 at 7:15 | comment | added | Ethan Dlugie | @PeterTaylor thank you very much for the code implementation! And to answer your question, the parts of the partition should be strictly between $0$ and $q$. A cone point of curvature $2\pi \cdot 0/q$ is actually a smooth point, and a cone point of curvature $2\pi \cdot q/q$ is actually a cylindrical end rather than a cone point. So your example is disallowed. | |
| Mar 8, 2023 at 23:40 | comment | added | Peter Taylor |
So you want to count partitions $\lambda \vdash 2q$ such that $\lambda_i + \lambda_j < q \implies (q - \lambda_i - \lambda_j) | q \vee \lambda_i = \lambda_j \wedge (q - \lambda_i - \lambda_j) | 2q$? If so then the additional thought gets you to $q = 100$ in seconds with fairly unoptimised code. However, I'm confused as to why the appendix of [3] doesn't list 4 1 1 1 1 for $q=4$ so it may be more complicated than I've understood.
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| Mar 8, 2023 at 17:55 | comment | added | Ethan Dlugie | @TimothyChow in fact for a given denominator $q$, the task would be to run through partitions of $2q$. So much worse! | |
| Mar 8, 2023 at 2:01 | comment | added | Timothy Chow | The number of partitions of 999 is 23127843459154899464880444632250 so whatever Thurston was doing, he certainly wasn't running through all these partitions one by one. | |
| Mar 8, 2023 at 1:38 | history | edited | Ethan Dlugie | CC BY-SA 4.0 |
Adding an extra comment with an approach to address one question
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| Mar 7, 2023 at 20:10 | history | edited | LSpice | CC BY-SA 4.0 |
Typo
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| Mar 7, 2023 at 20:07 | history | asked | Ethan Dlugie | CC BY-SA 4.0 |