Timeline for does this relation associated with a poset have a name?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Jun 5, 2023 at 13:50 | comment | added | mathematrucker | @მამუკაჯიბლაძე yes this dual pair of equations elegantly captures incomparability and optimality in one fell swoop...very nice! | |
| Jun 5, 2023 at 6:13 | comment | added | მამუკა ჯიბლაძე | @mathematrucker In this sense, yes, even smallest, resp. greatest, not just minimal, resp. maximal. In other words, necessary and sufficient conditions are ${\downarrow}(x)\setminus{\downarrow}(y)=\{x\}$ and ${\uparrow}(y)\setminus{\uparrow}(x)=\{y\}$, right? | |
| Jun 5, 2023 at 1:03 | comment | added | mathematrucker | @მამუკაჯიბლაძე assuming $x$ and $y$ are incomparable, the sense in which $x$ is minimal and $y$ maximal is that no point incomparable to $y$ is strictly less than $x$ (thus $x$ is minimal among such points) and no point incomparable to $x$ is strictly greater than $y$. | |
| Jun 4, 2023 at 22:08 | comment | added | Joel David Hamkins | @მამუკაჯიბლაძე You are right. I retract my comment (and have deleted). | |
| Jun 4, 2023 at 13:36 | vote | accept | mathematrucker | ||
| Jun 4, 2023 at 13:22 | history | edited | mathematrucker | CC BY-SA 4.0 |
removed ChatGPT content
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| Jun 4, 2023 at 11:23 | comment | added | Martin Rubey | This is now findstat.org/StatisticsDatabase/St001902 | |
| Jun 3, 2023 at 10:41 | comment | added | LSpice | I think that ChatGPT's answers to this question are irrelevant, at least as part of the question. (I would say that, if you really want to share them, then you can share them as an answer … but ChatGPT-generated answers are banned, so don't do that. In fact the linked post says that ChatGPT-generated content is banned, period.) | |
| Jun 3, 2023 at 3:17 | answer | added | Sam Hopkins | timeline score: 5 | |
| Jun 3, 2023 at 3:10 | history | edited | mathematrucker | CC BY-SA 4.0 |
added ChatGPT's 2c
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| Jun 1, 2023 at 17:53 | comment | added | mathematrucker | I think the relation deserves to be represented by more than just a symbol. | |
| Jun 1, 2023 at 17:49 | comment | added | mathematrucker | The biggest problem with envelope is that it's used for other things in other areas. Was hoping there would already be a name for this. That's looking very unlikely given the comment by @JoelDavidHamkins, which by the way might serve as a better foundation for the name than my definition in the question. | |
| Jun 1, 2023 at 14:54 | comment | added | mathematrucker | @AndreiSmolensky my so-called (for now, until someone suggests a better name) envelope is equivalent to a certain collection of partial orders, each of which not only contains the original partial order, but does so in a maximally snug fashion. | |
| Jun 1, 2023 at 6:17 | comment | added | Andrei Smolensky | "Envelope" is a strange name for a set that does not contain the original set. | |
| Jun 1, 2023 at 5:45 | history | asked | mathematrucker | CC BY-SA 4.0 |