# Tagged Questions

39 views

### How to describe any partition a set

For ignore of a better word, I will use word "partition" try to describe what I mean. How to describe partition(where over lapping subsets are allowed) of a set mathematically? In another word, ...
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### Generating functions of partition numbers

I don't understand at all why: $$\sum\limits_{n=0}^\infty p_n x^n = \prod\limits_{k=1}^\infty (1-x^k)^{-1}$$ Where $p_n$ is the number of partitions of $n$. Specifically ...
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### Probability distribution of product of integers

I have a scoring system based on 5 factors with integer values from 1 to 5: Score = A * B * C * D * E So the Score can range from 1 to 3125. Each of the factors ...
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### Conjugate Ferrers diagrams

Let $\pi=\langle \pi_1,\pi_2,... \rangle , \ \pi_1\ge\pi_2\ge...,$ be a partition of a number and $\pi'=\langle \pi_1',\pi_2',... \rangle$ be a partition conjugated to $\pi$, which means that ...
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### Number of equivalence relations on a finite set

I need a hint for computing the number of ways in which all the equivalent classes on a set of $n$ elements can be realized. For example, if the set has 2 elements ${a,b}$, then there are 2 possible ...
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### Partition an integer $n$ by limitation on size of the partition
According to my previous question, is there any idea about how I can count those decompositions with exactly $i$ members? for example there are $\lfloor \frac{n}{2} \rfloor$ for decompositions of $n$ ...
In how many ways one can decompose an integer $n$ to smaller integers at least 3? for example 13 has the following decompositions: \begin{gather*} 13\\ 3,10\\ 4,9\\ 5,8\\ 6,7\\ 3,3,7\\ 3,4,6\\ ...