Timeline for m-point-homogeneous, but not (m+1)-point-homogeneous
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2022 at 0:02 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
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| Nov 11, 2022 at 3:22 | answer | added | LeechLattice | timeline score: 3 | |
| Nov 10, 2022 at 18:31 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
added 219 characters in body
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| Sep 29, 2022 at 11:15 | comment | added | Anton Petrunin | @QiaochuYuan right, for me all of them are all-set-homogeneous. | |
| Sep 29, 2022 at 10:46 | comment | added | YCor | @QiaochuYuan for a space with $<n$ points, the $n$-point homogeneity rather sounds like an empty condition, hence true (however to make things reasonable one should allow non-injective families, or equivalently require, in the definition of $n$-homogeneity, $n'$-homogeneity for all $n'<n$). So, a finite set with all points at distance $1$ should be $n$-homogeneous for all $n$. | |
| Sep 29, 2022 at 3:38 | comment | added | Qiaochu Yuan | (Everywhere I refer to a polytope in what follows I mean its vertices regarded as a metric space with the $\ell^2$ norm.) Some googling found a paper (arxiv.org/abs/2206.13096) showing that the $n$-orthoplex is $2n$-point homogeneous (Corollary 4). It also contains the example that both the regular $n$-gon and the $n$-simplex are $n$-point homogeneous but they are not "not $n+1$-point homogeneous" in your sense since they don't have $n+1$ points at all. I can't find any examples in the paper which are $2k-1$-point homogeneous but not $2k$-point homogeneous for $k \ge 3$. | |
| Sep 28, 2022 at 20:53 | comment | added | Anton Petrunin | @WlodAA if you have an infinite one, then show it to me :) | |
| Sep 28, 2022 at 20:25 | comment | added | Wlod AA | Do you mean finite metric spaces? | |
| Sep 28, 2022 at 19:39 | history | asked | Anton Petrunin | CC BY-SA 4.0 |