# Questions tagged [multisets]

For questions about or related to multisets, a notion similar to sets with the difference that elements can be repeated.

249 questions
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### Can a Multiset product, mapping the relation x intersects y draw a roadmap

Can a multiset product ( like a cartesian product on sets) plotted with the relation x intersects y, draw a road map ? I tried this once before with sets (doesn't work with angling streets), but ...
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### Sets and Subsets

How many distinct subsets of the set $S=\{1,8,9,39,52,91\}$ have odd sums? Let, $O =$ Odd, and $E =$ Even. I figured, that only $\text{odd}+\text{even}=\text{odd}$, so I divided up the problem into ...
3answers
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### I am confused with braces inside braces. Please help me to figure out which are elements and which are sets in this set given in the picture . [closed]

Does 2 belongs to this set A? Does 2 an element of A..? (https://i.stack.imgur.com/Plc8B.jpg)
2answers
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### Simplification of a Finite Sum

For $m, n \in \mathbb{N}$, can $$\sum_{k=0}^{m} (m-k)! { m \choose m-k } { n \choose n - (m-k) } ( 1 - p)^{k} \cdot p^{m-k} \cdot \frac{ e^{-\lambda} \lambda^{n-(m-k)} } { (n - (m-k) )! }$$ be ...
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### Can I use inclusion symbol to address a multiset's elements?

Suppose a particular tree whose leaf elements are all objects $x$. Then, a collection $M$ represents the nodes of the tree (Obviously, $M$ is a multiset since it hosts $n$ repetitive objects $x$ for a ...
1answer
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### Permutation of a multiset with restrictions on two characters.

Consider the following: apples?and?oranges. I have to find the number of arrangements with the restriction that the two ? can't be together and they can't be located at the ends like ?...
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### Binary Entropy solving over uniform distributions

Compute the Binary Entropy for X is uniform over the set {1, 2, 3, . . . , 80} $$H(X) = -\sum_{i=0}^n p(x)log _2p(x)$$ I am pretty confused on this topic if someone could explain an easy way to ...
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### Mathematical notation for number of times an element appears in a multiset

I have a multiset, say $\{8,5,7,8,8,9,5,5,3,0,1\}$, and I wish to compute a weight with the following formula: number of times an element appears in the multiset divided by the total number of ...
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### Convolution formula for multisets coefficients

I've been trying to solve the following problem: (a) Give two proofs of the binomial coefficient identity, called the convolution formula, \$\sum_{j = 0}^k \binom{m}{j}\binom{n}{k - j} = \binom{m + n}...