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Jan 7, 2016 at 17:02 comment added Fedor Petrov Their upper estimate is stronger, because each polygon in $[0,n]^2$ has volume at most $n^2$. And lower estimate is much easier.
Jan 7, 2016 at 16:49 comment added Victor @FedorPetrov thanks for the reference to the paper by Bárány and Vershik you mentioned. If I understood well, their result doesn't directly imply something about the question. This is because not every polytope of 'proper' volume can be packed into $E_n$. For example if your try to apply their results to count the number of polytopes of volume $2n$, then some of these polytopes may be placed in $E_n$, but some may not (consider for example rectangle with sides 1 and $2n$).
Jan 7, 2016 at 16:40 comment added Victor Sure, in general, we may consider higher dimensions, but first I would like clearly understand basic case.
Jan 7, 2016 at 15:57 comment added Fedor Petrov The word "polytope" is for something more than 2-dimensional, is not it? By the way, asymptotical result is similar to that in dimension 2, done by Bárány – Vershik, renyi.hu/~barany/cikkek/52.pdf but it is not proved that limit constant exists
Jan 7, 2016 at 15:19 comment added Victor @Fedor, thanks for the answer. I need some time to understand your arguments, and I'm against closing the question at this point, as well.
Jan 7, 2016 at 13:32 comment added Fedor Petrov Hm. I am strongly against closing this question.
Jan 7, 2016 at 13:32 answer added Fedor Petrov timeline score: 3
Jan 7, 2016 at 6:20 answer added Douglas Zare timeline score: 1
Jan 7, 2016 at 5:11 review Close votes
Jan 7, 2016 at 9:47
Jan 7, 2016 at 1:01 history asked Victor CC BY-SA 3.0