All Questions
Tagged with multiset co.combinatorics
7 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 ...
- 34.3k
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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 ...
- 428
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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 $n$ ...
- 2,242
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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 ...
user120804
3
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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 ...
- 33
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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 ...
- 4,529
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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,...
