Timeline for What are efficient ways to compute the derivatives of iterated functions?
Current License: CC BY-SA 3.0
9 events
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| Mar 31, 2014 at 3:39 | comment | added | Yuval Filmus | Another approach would be to run a recursive procedure that accepts a "minimum" (originally 1), a "total" ($n$) and a "number" (originally $k$). If you pick $x$, you update the "minimum" to $x$, and in any case you decrease "number" by 1. | |
| Mar 31, 2014 at 1:59 | comment | added | Yuval Filmus | This is "selection with replacement". Perhaps the easiest way to approach this is via the standard bijection showing that the number of ways to choose $k$ out of $n$ with replacement is $\binom{n+k-1}{k}$. See the Wikipedia article: en.wikipedia.org/wiki/…. | |
| Mar 31, 2014 at 1:37 | comment | added | Daniel Geisler | Could you expand upon step 2. of your algorithm? Is there a name for tuples whose indices are only in lexicographically sorted order? I want to avoid having to enumerate all tuple indices and then discard the indices not in sorted order. | |
| Mar 27, 2014 at 21:39 | comment | added | Daniel Geisler | While I requested an efficient method of computing the derivatives of iterated functions, I also indicated that an effective algorithm for enumerating unordered hierarchical partitions, OEIS A000669, would be considered a solution. | |
| Mar 27, 2014 at 21:17 | vote | accept | Daniel Geisler | ||
| Mar 27, 2014 at 1:04 | history | edited | Yuval Filmus | CC BY-SA 3.0 |
added 41 characters in body
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| Mar 27, 2014 at 0:42 | comment | added | Daniel Geisler | The reference to a hierarchical partition of $n_i$ in the first point 2. should be an unordered hierarchical partition, shouldn't it? Unordered hierarchical partitions are enumerated by decomposing them into smaller unordered hierarchical partitions. Correct? | |
| Mar 27, 2014 at 0:32 | comment | added | Daniel Geisler | This is great, I have walked through it several times and see no problems. I'm going to attempt to implement this in Mathematica to verify that this works as intended. | |
| Mar 26, 2014 at 23:51 | history | answered | Yuval Filmus | CC BY-SA 3.0 |