| 25 Jul 2024 |
 rak1507 | yeah I don't think partial orders have anything to do with it | 01:12:06 |
| rak1507 | and "ordering" and "order" are also unrelated | 01:12:14 |
| rak1507 | permutations aren't generally ordered by order (now there's a sentence) | 01:12:28 |
 krftdnr | Well ain't that intuitive. | 01:12:39 |
| krftdnr | So when you want to number permutations you should just always be explicit about it and say the "Lehmer Code of the permutation" | 01:14:21 |
 discodoug | But Lehmer encoding gives them one!! There may be other systems. | 01:14:53 |
| discodoug | Either that or explain how your listing works. | 01:15:19 |
| krftdnr | Is there any mistake in my statement that assigning a total order to permutations is equivalent to numbering them? | 01:15:42 |
| discodoug | Any listing creates a total ordering but insisting there is one isn’t a ton of information. | 01:16:52 |
| rak1507 | yeah, you can have a bijection from permutations to integers | 01:17:03 |
| krftdnr | In fact there are probably a plethora of orderings possibly, since you can modify any ordering to get a new one. | 01:17:03 |
| rak1507 | n!! even | 01:17:13 |
| discodoug | I still recommend seeing how this is related to factorial base numbers. The math itself is fun. Not just the vocabulary. | 01:18:03 |
| discodoug | Actually you only need n! because you can embed permutations of k elements in permutations of n elements when k<n. | 01:31:08 |
| rak1507 | If there are n! permutations from 1 to n, aren't there n!! ways to order them | 01:32:48 |
| discodoug | Oh, sorry. I misread (and miscalculated) | 01:33:17 |
| rak1507 | Np | 01:33:28 |
 Marshall | To make matters more confusing, n!! usually means something different!! | 01:51:34 |
| Marshall | Not a big fan of that notation though, n!! being less than n! is weird. | 01:52:47 |
| rak1507 | lol true | 01:54:56 |
| rak1507 | Double factorials don't have too many applications so they seem pretty rare | 01:55:12 |
| rak1507 | From a brief look I don't think it has double factorials | 02:06:18 |
| krftdnr | Must not be that important then | 02:06:40 |
| krftdnr | Though it technically picked which to include based off properties of them, not which are useful. | 02:07:19 |
 coltim | wow "double factorial" is a comically bad name! | 12:13:05 |
 alexshroyer | strong biweekly vibes | 18:48:54 |
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| 26 Jul 2024 |
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| 27 Jul 2024 |
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