Timeline for A search for optimal order ideals
Current License: CC BY-SA 3.0
7 events
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 11, 2011 at 22:36 | comment | added | Victor Miller | @Gerhard: I fixed the typos (I think that I got all of them). One other thing: you can also define a different partial order on subsets of M: Say that $A \ge_D B$ if $f_A(t) \ge f_B(t)$ for all $t \in (0,1)$ (the $D$ is for dominates). It's necessary (but not sufficient) for $A$ to be maximal in this partial order (at least restricted to sets of cardinality $|A|$) in order for it to be optimal. I found empirically that almost all of the maximal sets for $N=64$ were optimal. | |
| Aug 11, 2011 at 19:22 | history | edited | Victor Miller | CC BY-SA 3.0 |
fixed a typo and added an explanation using bit-strings
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| Aug 11, 2011 at 19:11 | comment | added | Gerhard Paseman | Also, it is easy for me to get confused. A in M suggests that A is a set of numbers. A finite set A from M is a finite subset of M. By a finite set A in M I am guessing you mean the latter, but I would expect A subset M instead of what you have, which is A in M. Can I consider it a typo, and mentally substitue the subset symbol for the member of symbol in those places to get your meaning? Gerhard "Ask Me About System Design" Paseman, 2011.08.11 | |
| Aug 11, 2011 at 19:03 | comment | added | Gerhard Paseman | Thank you for showing this problem. I assume in the definition of A isomorphic to B you want B= instead of A=. Also, I apologize for an earlier error. The partial order I and Libor Polak used involved multisets, not sets, of the positive integers. I shall contemplate upon this problem. Gerhard "Ask Me About System Design" Paseman, 2011.08.11 | |
| Aug 11, 2011 at 18:54 | history | edited | Victor Miller | CC BY-SA 3.0 |
another typo
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| Aug 11, 2011 at 18:47 | history | asked | Victor Miller | CC BY-SA 3.0 |