Timeline for Visualizing diagrams needed to compute $\operatorname{Tr}(A^3 (A^T)^3)$
Current License: CC BY-SA 4.0
4 events
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| Mar 29 at 16:29 | comment | added | JimB | @azerbajdzan In short, I'm not arguing that the diagrams don't exist. But I think that they can be coalesced into the groupings I'm proposing if the objective is to find the combinations with positive expectations. The "test" will be if the finer grained diagrams provide a formula for the counts of occurrence and my approach doesn't. | |
| Mar 29 at 15:09 | comment | added | JimB | @azerbajdzan Good comment. My understanding of the objective is to find a general approach that allows for the determination of the expectation of the trace of certain functions of a matrix $A$ as defined above. My approach ends up with far fewer diagrams/cases as you've pointed out and I'll update my answer with a better description and rationale. What will matter in the end is the ability to count the occurrences of diagrams with positive expectations in some structured way which is essential but not even asked yet. | |
| Mar 29 at 12:55 | comment | added | azerbajdzan |
For d=1 there are 2 diagrams and your formula is {{2}} (which seems reasonable). For d=2 there are 5 diagrams and your formula is {{4},{2,2}}. For d=3 there are 19 diagrams and your formula is {{6},{4,2},{2,2,2}}. Can you explain how {{4},{2,2}} provides 5 diagrams and {{6},{4,2},{2,2,2}} provides 19 diagrams?
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| Mar 29 at 3:03 | history | answered | JimB | CC BY-SA 4.0 |