Timeline for Number of partitions of set restricted by sum of square of part size
Current License: CC BY-SA 4.0
33 events
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| S Sep 25, 2023 at 14:05 | history | bounty ended | CommunityBot | ||
| S Sep 25, 2023 at 14:05 | history | notice removed | CommunityBot | ||
| Sep 18, 2023 at 11:57 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 17, 2023 at 13:46 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 17, 2023 at 13:36 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 17, 2023 at 13:31 | comment | added | tony | @CommandMaster $L$ is increasing function of $n$ but it is fine if considering it as constant can make problem simpler. And $N(n)\in\{0,1,2,\cdots,\lfloor \frac{n^2-2\sqrt{2} n^{3/2}-2cn^{1+\epsilon}}{2} \rfloor\}$. | |
| Sep 17, 2023 at 13:28 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 17, 2023 at 13:25 | comment | added | tony | @CommandMaster There are two steps, first to partition the set $\{1,\cdots,n\}$, thus there are $\frac{n!}{\Pi_i (p_i!)^{a_i} \Pi_i a_i!}$ ways to do that; Second, for example $n=3$ and partition $\{1,2\}\{3\}$, denoted as $\{x_1,x_2\}\{x_3\}$, we want to assign values from $\{1,\cdots,L\}$ to them such that $x_1=x_2$ and $x_1\neq x_3$, $x_2\neq x_3$. Thus there are $\binom{L}{2}2!$ ways of assignments. | |
| Sep 17, 2023 at 13:21 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 17, 2023 at 13:13 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 17, 2023 at 12:56 | comment | added | Daniel Weber | Is $L$ a constant as $n\to\infty$? What about $N$? | |
| Sep 17, 2023 at 12:54 | comment | added | Daniel Weber | Just to make sure I understand the question: you want to estimate the number of partitions of $\{1,2,...,n\}$ such that there are $N$ pairs with both elements in the same part, and each partition is weighted $\frac{L!}{(L-m)!}$ where $m$ is the number of parts? | |
| S Sep 17, 2023 at 12:16 | history | bounty started | tony | ||
| S Sep 17, 2023 at 12:16 | history | notice added | tony | Draw attention | |
| Sep 17, 2023 at 12:11 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 15, 2023 at 15:39 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 15, 2023 at 11:37 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 15, 2023 at 9:31 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 15, 2023 at 8:38 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 15, 2023 at 8:18 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 15, 2023 at 8:07 | comment | added | tony | @DaveBenson Indeed, thank you! Now I added the motivation part. | |
| Sep 15, 2023 at 8:06 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 14, 2023 at 19:05 | comment | added | Dave Benson | The downvote not being mine, I'm just guessing, but it seems to me that the problem with this post is the equation barf without motivational text. Why are you interested, where did this come from, and what would it do for you? | |
| Sep 14, 2023 at 17:13 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 14, 2023 at 15:05 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 14, 2023 at 15:00 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 14, 2023 at 14:51 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 14, 2023 at 13:42 | comment | added | tony | @SeanSanford Thanks. but the expression in my post is exact, and I have no idea how to make the post less broad.. | |
| Sep 14, 2023 at 13:12 | comment | added | Sean Sanford | perhaps they thought your question was too broad in scope. fwiw this looks like you might want to search the term 'multinomial' | |
| Sep 14, 2023 at 13:02 | comment | added | tony | could the down-voted be explained so that I can improve my question? | |
| Sep 14, 2023 at 12:18 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 14, 2023 at 10:54 | history | edited | tony | CC BY-SA 4.0 |
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| Sep 14, 2023 at 10:40 | history | asked | tony | CC BY-SA 4.0 |