Timeline for Partitions and finite sets
Current License: CC BY-SA 3.0
10 events
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| Dec 8, 2017 at 17:10 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 3.0 |
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| Dec 7, 2011 at 11:49 | vote | accept | Taladris | ||
| Dec 7, 2011 at 6:00 | comment | added | Taladris | Thank you for your answers. I have a more precise question in mind but I need to think about it to formulate it properly. I will come back later. Anyway, your necessary conditions will help me to compute examples more efficiently. Thanks again. | |
| Dec 6, 2011 at 17:25 | comment | added | Aaron Meyerowitz | Roland makes a good point. We can restrict to the rational quotients which are at least 1. There must be a integers $U,V \gt 1$ such that $UV \ge n$, at least $U$ of the quotients occur with multiplicity $\ge V$ and at least $V$ of the quotients occur with multiplicity $\ge U$. In addition, given a quotient occurring with multiplicity $V$ (or $U$), the $2V$ (or $2U$) elements $c_k$ used in the numerator and denominators must have distinct indices | |
| Dec 5, 2011 at 17:13 | comment | added | Roland Bacher | A necessary condition: Some values among the $n(n-1)$ rational quotients of the form $c_k/c_{k'}$ with $k\not=k'$ must arise with multiplicity $\geq\sqrt{n}$. | |
| Dec 5, 2011 at 13:45 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
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| Dec 5, 2011 at 9:26 | comment | added | Pietro Majer | So everything reduces to the arithmetical condition on the $n$ lists of the exponents in the factorization of the numbers $c_k$ (assuming we have it). Given $n$ lists of non-negative integers $\gamma_k\in\mathbb{N}^m $ for $1\le k \le n$, the problem is to write them as $\alpha_i + \beta_j$ for some $\alpha_i \in\mathbb{N}^m $ and $\beta_j\in\mathbb{N}^m $. | |
| Dec 5, 2011 at 8:45 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
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| Dec 5, 2011 at 7:33 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
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| Dec 5, 2011 at 7:20 | history | answered | Aaron Meyerowitz | CC BY-SA 3.0 |