Timeline for Extending submodular functions from a sublattice
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2022 at 23:43 | history | edited | Geva Yashfe | CC BY-SA 4.0 |
Added details and also some newlines.
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| Aug 22, 2020 at 10:30 | comment | added | Geva Yashfe | That makes sense. I'll get to it within a couple of weeks and probably write to you directly - the comment thread feels like a bottleneck at this point. | |
| Aug 22, 2020 at 10:14 | comment | added | darij grinberg | Sure I wouldn't mind email. My problem is, the definition in Step 2 is just too... long. As I don't have any intuition for this subject, I can do nothing other than formal manipulations with such a definition. | |
| Aug 22, 2020 at 9:48 | comment | added | Geva Yashfe | @darijgrinberg I have not thought about it since June. I think the argument is probably correct, but I can go over it again and check more carefully, try to motivate it a little better. Would that help? Would you prefer to pass to email? | |
| Aug 21, 2020 at 12:37 | comment | added | darij grinberg | Have you found any simplifications in the meantime? I'm struggling with getting any clue on what's going on in Step 2... | |
| Jun 25, 2020 at 7:25 | history | edited | darij grinberg | CC BY-SA 4.0 |
align equations so I can print them better
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| Jun 22, 2020 at 5:37 | comment | added | darij grinberg | (I have not forgotten about this, just need to finish a few other things before I have the time to take a serious look at this.) | |
| Jun 13, 2020 at 21:19 | comment | added | Geva Yashfe | @darijgrinberg For those $A$'s as in the argument above: $A$ is contained in any set in $M$ that it intersects nontrivially. So this lattice only contains $M$ and the sets of the form $B \cup A$ for $B \in M$ (you can check this collection is closed under unions and intersections). | |
| Jun 13, 2020 at 20:27 | comment | added | darij grinberg | Because I'm too lazy to read up on lattice theory: What is "the lattice generated by $M$ and $A$" exactly, in the sense of, what is the simplest way to describe it? (I don't want to take nested intersections and unions...) | |
| Jun 13, 2020 at 13:23 | history | edited | darij grinberg | CC BY-SA 4.0 |
added 9 characters in body
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| Jun 12, 2020 at 23:51 | comment | added | Geva Yashfe | @darijgrinberg Well, I found a bug. It is fixed, but the new proof is more computational (this, and precise statement of the mistake, are in the edit). I am fairly certain that this suffices for your application to greedoids. Any comments are welcome. | |
| Jun 12, 2020 at 23:49 | history | edited | Geva Yashfe | CC BY-SA 4.0 |
Fixed a mistake. Unfortunately the new proof (while no longer clearly incorrect) is longer and more computational.
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| Jun 11, 2020 at 10:46 | comment | added | Geva Yashfe | @darijgrinberg and your application is cool! | |
| Jun 11, 2020 at 10:44 | comment | added | Geva Yashfe | @darijgrinberg I've added some further details in the last part. I think the argument is now complete (and as far as I see it is correct), so I'm done editing unless you spot some bug or have questions. This turned out longer than expected... | |
| Jun 11, 2020 at 10:42 | history | edited | Geva Yashfe | CC BY-SA 4.0 |
More details about modular pairs, filters
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| Jun 11, 2020 at 10:27 | comment | added | darij grinberg | Ah, I see. Will try to understand the argument now. | |
| Jun 11, 2020 at 10:27 | comment | added | Geva Yashfe | @darijgrinberg I don't think so: if $M$ is just a chain of sets, say $\emptyset \subset \{a\} \subset \{a,b\} \subset \{a,b,c\}$, steps of type $1$ can do nothing to make $\{b\}$ an element of $M$. | |
| Jun 11, 2020 at 10:25 | comment | added | darij grinberg | About the application to greedoids: See §4 of dropbox.com/s/bg2yw7dbjgxpkl3/stronggreed.pdf?dl=0 (the link will eventually rot, but it should be good for a month or two) for the question I'm trying to answer, and §7.2 for how I'm hoping to use Question 2 to achieve this. | |
| Jun 11, 2020 at 10:24 | comment | added | darij grinberg | I'm not sure I understand your plan: Shouldn't Step 2 be unnecessary, seeing that the lattice extension in Step 1 will eventually bring all subsets of $E$ into $M$ ? | |
| Jun 11, 2020 at 10:18 | history | edited | Geva Yashfe | CC BY-SA 4.0 |
Cosmetic changes for readability
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| Jun 11, 2020 at 10:07 | history | edited | Geva Yashfe | CC BY-SA 4.0 |
Added details and explanations
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| Jun 11, 2020 at 1:37 | history | edited | Geva Yashfe | CC BY-SA 4.0 |
Clarified a definition
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| Jun 11, 2020 at 0:59 | history | answered | Geva Yashfe | CC BY-SA 4.0 |