Questions tagged [multiset]
The multiset tag has no usage guidance.
12 questions
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3D generalization of Gaussian q-binomial coefficient
It is known that the coefficient of $q^t$ in Gaussian binomial coefficient $\binom{m+n}m_q$ equals the number of permutations of the multiset $\{0^m, 1^n\}$ with $t$ inversions.
Is there a closed ...
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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 ...
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Partitions of a multiset into equal parts
I am interested in a possible generalization of the following fact from combinatorics:
If $n<m$ then there are at least as many ways to partition a set of size $nm$ into $m$ sets each of size $n$ ...
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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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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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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 ...
CommunityBot
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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 ...
CommunityBot
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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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