Timeline for Sum of multinomals = sum of binomials: why?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 3, 2017 at 3:33 | vote | accept | T. Amdeberhan | ||
| Jun 3, 2017 at 2:26 | answer | added | Zach Teitler | timeline score: 13 | |
| Jun 2, 2017 at 21:50 | comment | added | T. Amdeberhan | I like the approach, Let's hope someone can pick up where you left off. | |
| Jun 2, 2017 at 21:49 | comment | added | Zach Teitler | $\binom{m+k-2j-1}{k-2j} = \dim S^{k-2j} \mathbb{C}^m$ so RHS = dimension of forms in $m$ variables, of degree $\leq k$, of degree same parity as $k$... no idea if that helps. | |
| Jun 2, 2017 at 21:42 | comment | added | T. Amdeberhan | Good idea. Perhaps the summand on the RHS becomes $\binom{m+k-2j-1}{k-2j}$. Then what? | |
| Jun 2, 2017 at 21:33 | comment | added | Zach Teitler | Set $m=n-2k$. Then $$ \binom{n-2k+j}{j,k-2j,n-3k+2j} = \binom{k-j}{j}\binom{m+j}{k-j} $$ and we sum over all values of $j$ (i.e., $0 \leq j \leq \lfloor k/2 \rfloor$ is the same as $0 \leq j \leq k-j$). | |
| Jun 2, 2017 at 18:07 | answer | added | Robert Israel | timeline score: 9 | |
| Jun 2, 2017 at 16:18 | history | asked | T. Amdeberhan | CC BY-SA 3.0 |