Timeline for Comparing partitions of a given planar convex region into pieces with equal diameter and pieces of equal width
Current License: CC BY-SA 4.0
10 events
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| Aug 28 at 6:05 | history | edited | Nandakumar R | CC BY-SA 4.0 |
correction in the title
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| Jan 12 at 10:06 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Jan 9 at 6:54 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Jan 8 at 12:15 | comment | added | Nandakumar R | It would help me gain some more clarity if you could show a specific example for some C and some small n wherein the two requirements can be met by different n-partitions of C. | |
| Jan 8 at 12:13 | comment | added | Nandakumar R | I meant: "for a C, there could be a set of n-partitions that maximize an equal width among pieces and another set of n-partitions that achieve min of equal diameter; will these two sets of partitions always have some intersection?" | |
| Jan 8 at 11:48 | comment | added | Beni Bogosel | I don't think the modification of the question adds something new... There is no reason to assume that the two partitions are the same for every convex C. | |
| Jan 8 at 11:39 | comment | added | Nandakumar R | Thank you. In view of your comment, just added a bit to the question. | |
| Jan 8 at 11:38 | history | edited | Nandakumar R | CC BY-SA 4.0 |
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| Jan 8 at 9:52 | comment | added | Beni Bogosel | I find extremely unlikely that the two problems you state should have the same optimal partition for general convex sets and general number of parts. I guess that "roughly speaking" for large $n$ the optimal partition will consist of patches of regular hexagons in both cases. However, it is likely that there exist perturbations of the shape $C$ which do not modify the width or diameter of one cell near the boundary while modifying the other one, contradicting simultaneous optimality. | |
| Jan 8 at 9:28 | history | asked | Nandakumar R | CC BY-SA 4.0 |