Timeline for How many different integer polytopes does square lattice have?
Current License: CC BY-SA 3.0
10 events
when toggle format | what | by | license | comment | |
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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 |