Timeline for Proving an identity about Catalan numbers
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 8, 2023 at 20:51 | vote | accept | banana | ||
| May 8, 2023 at 20:51 | vote | accept | banana | ||
| May 8, 2023 at 20:51 | |||||
| May 7, 2023 at 6:17 | comment | added | Fedor Petrov | if $j_1<j_2<\ldots<j_i$ are first elements of $i$ special pairs, then $j_1<j_2-1<j_3-2<\ldots <j_i-i+1\leqslant n-i+1$ are distinct numbers between 1 and $n-i+1$ | |
| May 7, 2023 at 4:49 | comment | added | Alapan Das | @banana Consider the $i$ pairs $j,j+1$ as $i$ boxes (which may includes $n+1$ as well). Now put the remaining $n-2i+1$ numbers can be arranged in $i+1$ ( the places in between the boxes and on the sides) in $\binom{n-i+1}{i}$ ways. | |
| May 6, 2023 at 23:59 | comment | added | banana | Could you explain why there are nCr (𝑛−𝑖+1, i) number of ways to choose 𝑖 special pairs? | |
| May 6, 2023 at 20:49 | history | answered | Fedor Petrov | CC BY-SA 4.0 |