Questions tagged [multisets]
For questions about or related to multisets, a notion similar to sets with the difference that elements can be repeated.
366 questions
0 votes
0 answers
62 views
combinatorics (multi-multi-choose-k)
I was studying a general way to solve problems like choose 4 words from word 'parallel' , or more generally choose r words from n words (where it may be distinct or identical ) and I came across r ...
- 1
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86 views
Is there a faster way of solving a multiset equation such that {-x,-y,-z,-xz,-xy,-xz,-xyz}={a,b,c,d,e,f,g} and others like it?
I was working with a multiset problem that can be solved by a system of nonlinear equations. The problem asks for what values of x and y are needed that satisfy the following multiset equation: $$\{ -...
- 153
1 vote
0 answers
47 views
Confusion of permutation of multiset
I have a problem understanding permutation of multiset. It is not about the number of such "permutation" or the list of them (I know the multinomial coefficients and the algorithm to list ...
- 11
0 votes
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70 views
Why does multiset theory struggle with a multiplicity of zero?
A multiset, $S$, can be represented by the set of pairs as follows: $$S=\{m_S(x_1)x_1,m_S(x_2)x_2,...,m_S(x_n)x_n\}$$ Where $m_S(x_i)$ is called the multiplicity of $x_i$ and is interpreted as the ...
- 141
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Selecting M sets / trajectories from a list N waypoints to maximize metrics around [M sets]
I have a list of 3d waypoints that i will call N=[w_0, w_1, w_2..]. My goal is to sample from N without replacement to form sets ...
- 386
2 votes
1 answer
264 views
Absolute difference in sum of AND and NOR of pairs of $1$s and $0$s
Let $A$ be a multiset of ordered pairs, having even cardinality, where all elements of ordered pairs are either $1$ or $0$, the number of times $1$ appears as a first element in the ordered pairs is $\...
- 311
0 votes
1 answer
116 views
do multi sets violate our axioms
I was talking with someone about solution sets for polynomials: I said $x\left(x - 1\right)=0$ and $x^{2}\left(x - 1\right) = 0$ has the same solution set $\left\{0,1\right\}$, but he said that you ...
0 votes
3 answers
111 views
Write down all the possible subsets of $A = \{∅\}$ and $A=∅$ [duplicate]
I am having trouble in finding the right answer to this because I'm not sure if $A = \{\varnothing\}$ and $A=∅$ are considered the same thing or not. Would the answer just be $∅$ for both cases or $\{\...
- 103
3 votes
1 answer
66 views
Distributing elements of a multi-set to triplets with certain properties possible?
Let $M$ be the multi-set which contains exactly $7$ copies of each positive integer from $1$ to $15$. That is, $M=${$1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,\ldots , 15,15,15,15,15,15,15$}. Is it ...
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-1 votes
1 answer
86 views
A hexadecimal number consists of the digits {0, 1, 2, 3, ... , 8, 9, A, B, C, D, E, F}. How many 5 digit hexadecimal numbers have exactly two letters? [closed]
Note: a hexadecimal number will not start with 0. The answer is 338,400. This question requires counting techniques (multi set, combination, permutation, product rule, etc.) to solve. The closest ...
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-1 votes
1 answer
164 views
Expressing Numbers Without Any Decimal Presumptions
I have long been uncomfortable with how numbers in alternative bases are expressed. Alternative bases are marketed as transcending our arbitrary base-$10$ conventions, but I wonder if they really ...
- 2,184
2 votes
1 answer
166 views
Multiset Matching
Suppose we have two multisets of positive integers, $A$ and $B$, where the sum of the elements (counted with multiplicity) of the two multisets is the same. Starting from $A$, we would like to arrive ...
0 votes
0 answers
26 views
Size of a Power Set of a Multiset where some items are Indistinguishible [duplicate]
Note: I do not know all the terminology for my question, so I am making some educated guesses. Please let me know the correct terminology for anything I get the name of wrong. Suppose I have a ...
- 101
2 votes
0 answers
68 views
Image of the standardization of permutations of a finite multiset
Let $M$ be a multiset $\{1^{m_1},2^{m_2},...\}$ whose cardinality $\#M:=m_1+m_2+...=:n$. Let $\Sigma:S_M\to S_n$ be the standardization map defined in Stanley combinatorics volume 1 ($S_M$ is the set ...
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396 views
20 identical red balls, 20 identical blue balls, 20 identical green balls, 1 white ball, and 1 black ball. You draw 15. How many outcomes?
A bag contains 20 identical red balls, 20 identical blue balls, 20 identical green balls, 1 white ball, and 1 black ball. I reach in to get 15 balls. How many outcomes are there? The problem came from ...
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