Timeline for finding permutations which fulfills given conditions
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| Oct 22, 2011 at 13:09 | history | tweeted | twitter.com/#!/StackCSTheory/status/127733263988035584 | ||
| Oct 20, 2011 at 6:50 | comment | added | Suresh Venkat | @KostiaAntoniuk: I see. but to be honest, your first question was very cryptic. This one makes more sense :) | |
| Oct 20, 2011 at 6:33 | comment | added | Kostia Antoniuk | Jukka Suomela, I think your interpretation is correct. | |
| Oct 20, 2011 at 6:29 | comment | added | Kostia Antoniuk | Suresh Venkat, I have already asked about this here in terms of finding such permutations to make the problem submodular one, but nobody gave answer on this. Thus, I decided to make such formulation, and as you see, there is some answer given by Yoshio Okamoto. | |
| Oct 20, 2011 at 1:42 | answer | added | Yoshio Okamoto | timeline score: 4 | |
| Oct 19, 2011 at 23:35 | comment | added | Jukka Suomela | Another interpretation might be this: can we permute the rows and columns of a matrix to make it "supermodular"? (Again, assuming that the "if and only if" part is wrong.) | |
| Oct 19, 2011 at 23:19 | history | edited | Jukka Suomela | CC BY-SA 3.0 |
we are not running out of letters yet; no need to use combinations of subscripts and primes...
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| Oct 19, 2011 at 23:05 | comment | added | Yoshio Okamoto | I'm concerned with "if and only if" in the REFORMULATION. For example, if g is a constant function, g is supermodular. But the condition in the REFORMULATION is not satisfied because for all 4-tuples (k1,k2,k1',k2') the inequality is satisfied (with equality). | |
| Oct 19, 2011 at 22:55 | comment | added | Suresh Venkat | In fact I'd recommend changing the title given this observation. | |
| Oct 19, 2011 at 22:33 | comment | added | Suresh Venkat | It's worth noting that in the lattice induced by the product order of $A_1$ and $A_2$, the point $(k_2, k'_2)$ is the meet of $(k_1, k'_2), (k_2, k'_1)$ and the point $(k_1, k'_1)$ is the join. So actually your condition is merely the definition of supermodularity for $g$. So rephrased, your question is: Is there a way, for any function $g$, to construct a product lattice from two total orders so that $g$ is supermodular ? | |
| Oct 19, 2011 at 22:25 | history | edited | Suresh Venkat | CC BY-SA 3.0 |
added 8 characters in body
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| Oct 19, 2011 at 22:07 | comment | added | Kostia Antoniuk | Yes, you understood it correctly! | |
| S Oct 19, 2011 at 20:26 | history | suggested | Gopi | CC BY-SA 3.0 |
I modified the question so it can be clearer. I left the first question untouched in case my understanding of the meaning was wrong
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| Oct 19, 2011 at 17:53 | comment | added | Gopi | I have submitted an edit of the question so it is clearer (the way I understood it). If that was not the initial meaning of the question you can delete it: I have left your question untouched. | |
| Oct 19, 2011 at 17:52 | review | Suggested edits | |||
| S Oct 19, 2011 at 20:26 | |||||
| Oct 18, 2011 at 18:56 | history | edited | Suresh Venkat | CC BY-SA 3.0 |
added 29 characters in body
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| Oct 18, 2011 at 17:11 | history | asked | Kostia Antoniuk | CC BY-SA 3.0 |