Timeline for A seemingly simple combinatorial object that must have an easy generating function
Current License: CC BY-SA 3.0
13 events
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 13, 2016 at 19:29 | answer | added | მამუკა ჯიბლაძე | timeline score: 5 | |
| Feb 29, 2016 at 0:36 | answer | added | მამუკა ჯიბლაძე | timeline score: 1 | |
| Feb 10, 2016 at 16:59 | comment | added | მამუკა ჯიბლაძე | @LiorSilberman No no it is as intended. "Geometrically" it is really the midpoint: a composition $(a_1,...,a_k)$ of $n$ is more or less the same as a partition of the set $\{1,...,n\}$ of points of the real line into disjoint subsets of contiguous points, $\{1,...,a_1\}$, $\{a_1+1,...,a_1+a_2\}$, $\{a_1+a_2+1,...,a_1+a_2+a_3\}$, ..., $\{a_1+a_2+...+a_{k-1}+1,...,n\}$. Then the midpoint of $\{1,...,a_1\}$ is $\frac{a_1+1}2$, the midpoint of $\{a_1+1,...,a_1+a_2\}$ is $a_1+\frac{a_2+1}2$, etc. | |
| Feb 10, 2016 at 16:30 | comment | added | Lior Silberman | Typo in the definition of midpoint: $a_i+1$ should be $a_{i+1}$ | |
| Feb 10, 2016 at 15:36 | answer | added | Max Alekseyev | timeline score: 10 | |
| Feb 10, 2016 at 10:10 | comment | added | Martin Rubey | For what it's worth, here are some more terms: $1, 3, 12, 39, 142, 480, 1701, 5855, 20510, 71090, 247998, 861723$. Note that the numbers have huge prime factors. Eg. $861723 = 9\cdot 95747$ | |
| Feb 9, 2016 at 16:15 | comment | added | Timothy Chow | If you think there is a simple generating function then one thing you can try is to generate more terms and use something like Maple's guessgf (in its gfun package) or Mathematica's FindGeneratingFunction. | |
| Feb 9, 2016 at 6:24 | comment | added | მამუკა ჯიბლაძე | @TimothyChow In that case it is very easy to show that the sequence is $3^{n-1}$. This is one of the reasons I hope that there must be a good generating function. | |
| Feb 9, 2016 at 3:30 | comment | added | Timothy Chow | If you change the definition of mid to $\{a_1 + \cdots + a_i \mid 1 \le 1\le k-1\}$ then does OEIS give you anything? | |
| Feb 8, 2016 at 18:08 | comment | added | მამუკა ჯიბლაძე | @TonyHuynh Oh I should mention this, I've looked there too, also for the sequence divided by 2 (obviously all the numbers are even). I thought about adding it but first I want to learn more about it | |
| Feb 8, 2016 at 18:01 | comment | added | Tony Huynh | I checked oeis.org and your sequence is not in the database. | |
| Feb 8, 2016 at 10:56 | history | asked | მამუკა ჯიბლაძე | CC BY-SA 3.0 |