Talk:Ordered partitions

Incorrect math statement

The task says:

Note that the number of elements in the list is

$({\mathit {arg}}_{1}+{\mathit {arg}}_{2}+...+{\mathit {arg}}_{n}\ \mathrm {choose} \ arg_{1})*({\mathit {arg}}_{2}+{\mathit {arg}}_{3}+...+{\mathit {arg}}_{n}\ \mathrm {choose} \ {\mathit {arg}}_{2})*\ldots *({\mathit {arg}}_{n}\ \mathrm {choose} \ {\mathit {arg}}_{n})$

But this cannot be right.

The task with args 1,2,4 would generate 105 distinct partitions. But 4 choose 1 is 0 and 4 choose 2 is 0 and 4 choose 4 is 1, so the above formula would give a result of 6. --Rdm 22:27, 7 February 2011 (UTC)

Never mind, I fixed it. --Rdm 22:36, 7 February 2011 (UTC)

Is it really fixed? As far as I know choose, the bigger number should be on the left. Anyways, I'll change it to

${{\mathit {arg}}_{1}+{\mathit {arg}}_{2}+...+{\mathit {arg}}_{n} \choose {\mathit {arg}}_{1}}\cdot {{\mathit {arg}}_{2}+{\mathit {arg}}_{3}+...+{\mathit {arg}}_{n} \choose {\mathit {arg}}_{2}}\cdot \ldots \cdot {{\mathit {arg}}_{n} \choose {\mathit {arg}}_{n}}$

to make it clearer --Eugen 10:36, 8 February 2011 (UTC)

Oh! No, the original page was right, and I was wrong, about that left vs. right thing with the word "choose".

My problems were twofold: First, I did not have a definition of "choose", and second I did not know how to group operations when faced with a + b choose c. I went with a + (b choose c), but it's now clear to me that I should have gone with (a+b) choose c. The current main page shows operator precedence clearly, but still could do with a link to a definition. (The link to Combinations suggests a definition, and there can be good reasons to order the arguments that way, but that does not actually define the operation the original (anonymous) author intended for choose. Perhaps the right approach here would be to mention popular notation issues on the Combinations page?) --Rdm 15:55, 8 February 2011 (UTC)