(Reply) [entries|reading|network|archive]

[ userinfo | dreamwidth userinfo ]
[ archive | journal archive ]

[personal profile] jack Tue 2014-03-11 15:12
A more specific conjecture would be that any optimal dissection (in your extended criterion of tie-breaking) of a set of n m-sized sticks and a set of m n-sized sticks into two identical piles of fragments can be performed by a sequence of "Divide (the remainder of) some stick from one set into N (N>=1) equal sized fragments, and removing the corresponding fragments from sticks in the other set. Then repeat, dividing one of the new remainders, until nothing is left."

I don't think that's worded quite right, but I think something like that. If so, maybe a perturbations argument could show that if at some step you divide into the same number of fragments of slightly different lengths, you can follow through the remainder of the steps in the same way. And if so, the non-equal division would be sub-optimal (because one stick of that length gets shorter).

But I'm not sure if that's actually right, or just another plausible guess that will turn out to have exceptions.
Link Read Comments
Anonymous( )Anonymous This account has disabled anonymous posting.
OpenID( )OpenID You can comment on this post while signed in with an account from many other sites, once you have confirmed your email address. Sign in using OpenID.
Account name:
If you don't have an account you can create one now.
HTML doesn't work in the subject.


Notice: This account is set to log the IP addresses of everyone who comments.
Links will be displayed as unclickable URLs to help prevent spam.