Can someone please proof how number of permutations of first N natural numbers with no three-term increasing subsequence can be given by the Nth catalan number .. ?
More formally number of permutations such that there doesn't exist any i<j<k for which a[i]<a[j]<a[k].
| № | Пользователь | Рейтинг |
|---|---|---|
| 1 | tourist | 3690 |
| 2 | jiangly | 3647 |
| 3 | Benq | 3581 |
| 4 | orzdevinwang | 3570 |
| 5 | Geothermal | 3569 |
| 5 | cnnfls_csy | 3569 |
| 7 | Radewoosh | 3509 |
| 8 | ecnerwala | 3486 |
| 9 | jqdai0815 | 3474 |
| 10 | gyh20 | 3447 |
| Страны | Города | Организации | Всё → |
| № | Пользователь | Вклад |
|---|---|---|
| 1 | maomao90 | 173 |
| 2 | awoo | 164 |
| 3 | adamant | 163 |
| 4 | TheScrasse | 160 |
| 5 | nor | 157 |
| 6 | maroonrk | 156 |
| 7 | -is-this-fft- | 152 |
| 8 | Petr | 146 |
| 8 | orz | 146 |
| 10 | pajenegod | 145 |
Catalan Number is the number of different ways a convex polygon with n + 2 sides can be cut into triangles by connecting vertices with straight lines (a form of Polygon triangulation).Try to find similarity between your problem and this problem. I do not have any formal proof as of now. Hope it helps.
https://math.stackexchange.com/questions/155867/penguin-brainteaser-321-avoiding-permutations
check this