# Questions tagged [multiset]

The multiset tag has no usage guidance.

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### Does there exist a canonical form for normal matrices which extends the following embedding?

Given an unordered pair of complex numbers $\{w,z\}$, we can associate to it the complex matrix
$$\frac 1 2\left[\begin{matrix}w + z + \frac{\left(w - z\right)^{2} + \left|{w - z}\right|^{2}}{2 \left|{...

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### Counting multisets satisfying a fixed property

Suppose $S$ is a infinite set and $R\subset S$ is also infinite. Now, we want to find the number of multisets $(M,\nu)$, with $M\subset S, |(M,\nu)|=n$, and having an additional property that for ...

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### An equation involving multisets

For finite multisets $A, B, C, A', B', C'$, if $A \uplus B \uplus \{B \uplus C\} \uplus \{A \uplus \{C\}\}$ = $A' \uplus B' \uplus \{B' \uplus C'\} \uplus \{A' \uplus \{C'\}\}$, must $A=A',B=B',C=C'$, ...

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### The category of Multisets and Spans: morphism composition and tensor product

I have been thinking about multisets for a while. These are sets where elements can repeat, so $S =\{ a,a,b,c,b\}$ is a multiset on the set $A = \{a,b,c\}$.
I have also been looking into morphisms ...

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### The combinations of a finite multiset [closed]

Suppose there is a basket $S$ containing $3\ \color{blue}{blue}$, $2\ \color{green}{green}$ and $1\ \color{red}{red}$ balls. A subject can extract any $k$ number of balls (including $0$) at random ...

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### Counting Specific Permutations of Elements in a Multiset

I have a question regarding counting permutations of a multiset's elements. The problem is the following:
Given a multi-set $M=\{0^{m}, 1^{n-m}\}$ the number of all possible permutations of its ...

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### What is the fastest way to sort numbers lexicographically?

I have $N$ sequences of numbers. None of them is longer than $10^6$. I want to sort those sequences lexicographically. For example, given sequences {1, 2, 4}, {1, 2, 3}, {2, 5, 7}, {2}, I want to have ...

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### A natural sum over multisets (expectation over multinomial)

I think this is a natural question but am not sure where to find resources.
Consider the possible multisets arising from choosing $n$ times an item from one of $k$ categories. We can represent one ...

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### Generating all derangements of a multiset?

I'm trying to find a reference to an algorithm for generating all the derangements of a multiset (this is not my area of expertise, by the way!), and so far I have found plenty on derangements of sets,...

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### What is the "correct" category of multisets

During seminar the other day, when speaking about subobject classifiers, I asked if the subobject classifier for the category of multisets would have integer truth values, corresponding to the number ...