Have you yet found an example where the (apparent) optimal solution requires dividing any stick into more than three pieces?
Is there any good reason not to consider wlog m<n?
Beyond that, I'm too woozy at the moment, which is a pity as this problem is going to bug me without my getting much traction on it!
Have you yet found an example where the (apparent) optimal solution requires dividing any stick into more than three pieces?
No, but I haven't looked at any especially large examples, and that's where I'd most expect to see large dissections. I was rather hoping to find a sensible search algorithm and then run it on lots of pairs to collect data for a conjecture, but so far I haven't thought of a good criterion for the search algorithm figuring out when it can be sure all subsequent solutions it finds will be worse.
Is there any good reason not to consider wlog m<n?
None at all – the problem is certainly symmetric in m,n.
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Is there any good reason not to consider wlog m<n? Beyond that, I'm too woozy at the moment, which is a pity as this problem is going to bug me without my getting much traction on it!
No, but I haven't looked at any especially large examples, and that's where I'd most expect to see large dissections. I was rather hoping to find a sensible search algorithm and then run it on lots of pairs to collect data for a conjecture, but so far I haven't thought of a good criterion for the search algorithm figuring out when it can be sure all subsequent solutions it finds will be worse.
Is there any good reason not to consider wlog m<n?
None at all – the problem is certainly symmetric in m,n.