Timeline for A variant of the capset problem
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 24, 2023 at 16:32 | comment | added | Eric Naslund | @SeanEberhard: The Partition Rank solves point 2, and reduces it to point 1 without causing degree issues. However, point 1 is a problem. It suffices to observe that if two of your equations are trivially solved, then so is the third. Using the delta notation in my paper, consider your tensor multiplied by $$(1-\delta(x,y,a)-\delta(x,z,b)-\delta(y,z,c)).$$ The term involving $\delta(x,y,a)$ must have $b=c$, and so it is equivalent to multplying by $\delta(x,y,a)\delta(b,c)$ and the Partition Rank Method provides a bound. The problem is the $1$ term - i.e. the original tensor | |
| Jun 5, 2020 at 11:15 | comment | added | Sean Eberhard | To clarify, I think that probably solves my point 2, in some sense, but only at the cost of pushing the degree of configuration tensor up even higher, so my point 1 is as problematic as ever. | |
| Jun 5, 2020 at 11:09 | comment | added | Sean Eberhard | Oh I see, he builds the distinctness into the tensor rather than deal with the partial degeneracy latter. Interesting, will investigate. | |
| Jun 5, 2020 at 10:22 | comment | added | Thomas Bloom | Eric Naslund (arxiv.org/pdf/1701.04475.pdf) came up with a generalisation of slice rank to 'partition rank' to deal with a similar problem where it was morally of complexity 1, but there are partially degenerate solutions. Have you tried running this problem through the more general partition rank machinery? | |
| Jun 5, 2020 at 8:09 | history | asked | Sean Eberhard | CC BY-SA 4.0 |