The multisets tag has no wiki summary.
1
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1answer
53 views
Is this a tricky math question?
[EDIT]
If $a = \{1,2,3\}$ and $b = \{a,b,c\}$ FIND n(axb)
or is it impossible to multiply these?
What will be the answer
1
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2answers
34 views
Proper way to define this multiset operator that does a pseudo-intersection?
it's been a while since I've done anything with set theory and I'm trying to find a way to describe a certain operator.
Let's say I have two multisets:
$A = \{1,1,2,3,4\}$
$B = \{1,5,6,7\}$
How ...
3
votes
3answers
84 views
Is there such a thing as a multiset with a “negative” number of some element?
Is it possible for a multiset to have a "negative" number of one or more elements? If so, how are such multisets defined, and what terminology exists for them?
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2answers
41 views
How to make precise the notion of “the multiset of roots of a polynomial function”?
A (real) polynomial function can be defined as a function $f : \mathbb{R} \rightarrow \mathbb{R}$ such that there exists a sequence $a : \mathbb{N} \rightarrow \mathbb{R}$ such that the terms of $a$ ...
6
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2answers
102 views
Combinatorial proof for identity $\left(\!\!\binom{n\vphantom{1}}{k}\!\!\right)=\left(\!\!\binom{k+1}{n-1}\!\!\right)$ (multiset coefficients)
In class we have recently started using combinatorial proofs. I have tried this problem that our teacher has assigned as a "challenge". I understand how to receive the left hand side, but am ...
0
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0answers
37 views
Which definitions for set-builder notation exist for multiset theory?
Interesting cases would be
$A=[1,1], B=[2]$
$[(a,b) \mid a \in A \wedge b \in B] = [(1,2),(1,2)]$ ?
or
$C=[1,2,3]$
$[x \mid c \in C \wedge x = c \mod 2] = [1,0,1]$ ?
The only kind of informal ...
1
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0answers
45 views
Set-valued map (measurability)
I have this exercice and i want to know how to solve it :
1)- Let $X,Y$ two separable metric spaces ,let $(\Omega, \mathcal{A})$ be a measurable space ,and $f: \Omega \rightarrow X$ a measurable ...
0
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0answers
52 views
Is it possible to find a formula for a set of number from the result?
I have these two sets of number, I also have a result. Is it possible to compute the relation between them so that I can figure out how the result is generated ?
for example I have :
Set A=4 6 12 25 ...
1
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1answer
67 views
Difference between inclusion-exclusion problems
There are two situations.The first is a bakery which has three type of doughnuts, {6*chocolate , 6*cinnamon, 3*plain}. How many options do they have for a box of 12 doughnuts?
The second question is ...
1
vote
1answer
34 views
Probability of an item being selected in a multiset
I would like to know that probability of an item occurring in a multiset (a combination of selections with repetitions).
Given a set $S = \{x_1,x_2,...,x_n\}$ the number of possible unordered subsets ...
2
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1answer
110 views
Combinatorics/Multisets problem question
I wonder how a problem of the following type can be solved. I have looked for a solution but I am not to identify the kind of problem I am facing. I would like to know if there is a close formula or ...
6
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0answers
119 views
A variation on the Look and Say Sequence and some questions about it.
For information on the sequence mentioned in the title, see http://en.wikipedia.org/wiki/Look-and-say_sequence. This is an original problem.
Suppose instead of "describing" the numbers in a string in ...
1
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3answers
127 views
Combinations of multisets - the theory?
I've read over the theory countless times, and I still have no idea how to think of it.
The formula for the combinations of multisets is C(k + r - 1, r), where k = the number of distinct elements, ...
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0answers
13 views
Split N integers into M groups such that the difference of each's sum is as small as pos [duplicate]
Possible Duplicate:
Put N items into M groups such that the sums of the N’s in every M are as even as possible
Speaking in programming terms in which I can articulate myself more clearly, I ...
0
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1answer
84 views
Put N items into M groups such that the sums of the N's in every M are as even as possible
I have a multiset, S, that contains N items that I wish to place into ...
1
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1answer
188 views
Probability of predicting, then throwing, a particular multiset for 5 dice.
My friend shared with me a story that after losing to his SO at Yahtzee, before they put the game away he just randomly predicted he would roll four 5's and a 1. He then got that roll and freaked out.
...
1
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1answer
86 views
Number combinations multi set
Here is my question:
Consider a multiset $\{n\cdot a, n\cdot b, 1,2,3, \ldots, n+1\}$ of size $3n+1$. Determine the number of $n$-combinations.
I know from my textbook that if you have a ...
0
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0answers
34 views
Set building formal notation question
So I'm trying to express a very simple algorithm mathematically using sets. What I want to express is the following:
Given a multiset $X$ which contains further multisets, $Z_Y = \{ f(x) : x \in Y ...
1
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1answer
122 views
Are lexicographic and multiset the only extensions of sets that preserve well-foundedness?
It is well known that for a given set $S$ with well-founded order relation $R$, the lexicographic order that extends $R$ on tuples of $S$ is also well-founded.
Also, the multiset order on the ...
46
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5answers
1k views
Why does mathematical convention deal so ineptly with multisets?
Many statements of mathematics are phrased most naturally in terms of multisets. For example:
Every positive integer can be uniquely expressed as the product of a multiset of primes.
But this ...
1
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1answer
122 views
What is the notation for the multisets of R?
The set of sets of elements of $R$, also known as powerset of $R$ can be typeset $2^R$. I am now interested in the set of multisets of elements in $R$. How is it called? Is there a standard notation?
1
vote
1answer
191 views
Number of k-combinations of a multiset
Say that I'm buying cakes for a party. I wish to buy $k$ cakes, and there are $n$ different kinds of cake, but only $m_i$ of each kind of cake (where $i$ denotes the $i$th kind). How many different ...
0
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1answer
128 views
Derangements of multisets
Find the number of ways string of numbers (may contain similar items) could be deranged so that a number is not placed in the same place as it or its similar numbers were placed.
For example, ...
1
vote
3answers
240 views
Multiset Combination in Combinatorics
I want to buy a $k$-combination of doughnuts, where $k$ is any amount less than or equal to the total doughnuts available. At the bakery there are $n$ different types of doughnuts but there are ...
5
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2answers
149 views
permutations of a multiset having symbols with fixed multiplicity
Let $N$ be a multiset of $n$ distinct objects having the same multiplicity $k$. For instance,
$N=\{a,\,a,\,b,\,b\}$
where $n=2$ and $k=2$.
I was looking for the problem of counting the number of ...
8
votes
1answer
403 views
What is the number of bijections between two multisets?
Let $P$ and $Q$ be two finite multisets of the same cardinality $n$.
Question: How many bijections are there from $P$ to $Q$?
I will define a bijection between $P$ and $Q$ as a multiset $\Phi ...
4
votes
2answers
142 views
Probability of throwing the same multiset twice in a row with six dice
Six dice are thrown. The six dice are thrown a second time. What is the probability of getting the same numbers as in the first throw? If the order of the six numbers matters, the problem is easy, but ...
1
vote
1answer
60 views
How many natural multisets exist with a given sum?
Given natural number $n$, how many multisets are there which sum of their elements equals $n$?
There is a recursive function which can give the value in $O(n^2)$, but is there a formula for that?
...
2
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0answers
251 views
Permutations of Subsets of a Multiset
What is the number of permutations of subsets of the multiset $S$ with cardinality $n$? A sample problem would be, say, to find the number of ways can you make "words" with three of the letters in the ...
2
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1answer
61 views
Identity of generating function of weights of multiset cycles.
A few days ago I asked this question on a generating function of multiset cycles.
There is was shown that $\prod_C(1-w(C))^{-1}=\sum_{\pi}w(\pi)$ where $w(\pi)$ is the weight a a multiset permutation ...
1
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1answer
205 views
Generating function of multiset cycles?
I've been tossing the idea of multiset cycles around in my head for the past day or two. In Stanley's Enumerative Combinatorics, he defines a multiset cycle to be a sequence $(i_1,i_2,\dots,i_k)$ of ...
-4
votes
1answer
316 views
partition of a multiset
Let $X=\{\underbrace{a_1,\cdots ,a_1}_{\nu_1},\cdots,\underbrace{a_k,\cdots ,a_k}_{\nu_k}\}$
be a multiset of cardinality $\sum{\nu_i}=n$ where each $a_i$ repeats $\nu_i$ times. We suppose that when ...
2
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2answers
708 views
Compute the number of different sums that can be created by adding the elements of a set
Example set {9, 6}.
I am creating multisets of cardinality 3 out of its elements, for example, {9, 9, 6}.
How do I compute the number of different sums that can be created by adding the elements of ...
0
votes
1answer
41 views
The proportion between distinct labels in a multiset and the total amount of labels
Say we have a (multi)set $\alpha$ of $n$ balls, each of them is labeled with a number in $\{1,\ldots,m\}$ (where $m<n$ ).
Denote by $d$ the amount of distinct labels in $\alpha$. Is it true that ...
4
votes
2answers
570 views
Number of combinations of a multiset of objects
Determine the total number of combinations (of any size) of a multiset of objects of $k$ different types with finite repetition numbers $n_1, n_2, \ldots, n_k$ respectively.
The answer is ...
0
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1answer
268 views
Multiset Notation
There is a multiset $A$, of length $n$ that can contain only $1s$ or $0s$. How would I notate that? How about for a multiset that could contain any number from $1-1000$, or that could contain any real ...
5
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3answers
220 views
Number of possible sets for given N
How many possible valid collections are there for a given positive integer N given the following conditions:
All the sums from 1 to N should be possible to be made by selecting some of the integers. ...
3
votes
4answers
171 views
How many distinct multiplications?
I have a multiset $\left\{ {2,3,3,3,4,4,5,5,6,7} \right\}$. How many distinct multiplications of three numbers chosen from the multiset?
e.g. $2×3×3$; $2×3×4$; ...
0
votes
1answer
186 views
Multiset indicator function
I'm writing a report and was wondering wheter my notation is understandable? I'm fairly new to using the maths notation. A similarity measure between a multiset $u$ and a set $c$ is defined as:
...
2
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1answer
170 views
Probability of having 'k' elements that occur only once in a multiset filled by sampling with replacement
Let's say that I have a set of unique elements, $P$, and a multiset $M$ that I fill with $N \leq ||P||$ elements by sampling with replacement from $P$. What is the probability that the multiset $M$ ...
6
votes
1answer
179 views
What is the number of ways to choose x groups from y items? (partitions with x cells of a multiset)
Where a group can consist of 1 or more items, groups don't have to be equally sized and items can be duplicates. Example - Choose 3 groups:
Items: 1 2 2 3
Groups:
(1) (2 2) (3)
(1 2) (2) (3)
(3 ...
2
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2answers
110 views
Is 2-multiset a valid term?
I am trying to describe the edges of an undirected graph that contains loops. On Wikipedia they are characterized as 2-multisets, meaning it has two elements which can be identical, and the order is ...
2
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3answers
215 views
Set vs Multiset
A set is a collection of distinct objects.
Suppose I sample some parameter of some population and the results are $\{35,35,36,36,37 \}$.
Do I need to say (i) the multiset of the samples is $\{35,35, ...
5
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4answers
337 views
How to find unique multisets of n naturals of a given domain and their numbers?
Let's say I have numbers each taken in a set $A$ of $n$ consecutive naturals, I ask myself : how can I found what are all the unique multisets, which could be created with $k$ elements of this set ...
4
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3answers
341 views
Stirling numbers of the second kind on Multiset
Stirling numbers of the second kind S(n, k) count the number of ways to partition a set of n elements into k nonempty subsets.What if there were duplicate elements in the set?That is,the set is a ...
5
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1answer
192 views
Odd number of reals with equal partitions
Consider the following problem:
You are given a multiset (a set with repetitions allowed) of $2n+1$ real numbers, say $S = \{r_1, \dots, r_{2n+1}\}$.
These numbers are such that for every $k$, the ...
2
votes
2answers
498 views
An efficient method for computing the number of submultisets of size n, of a given multiset
There are a number of ways to describe this problem. I shall name a few.
Submultisets
Let $(M, f)$ be a multiset where $M = {x_1, ... x_k}, |M| = k$ and $f(x_i) = m_i$, i ranging from 0 to k ...
6
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2answers
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Permutations with identical objects
How can I find the number of k-permutations of n objects, where there are x types of objects, and r1, r2, r3 ... rx give the number of each type of object?
Example:
I have 20 letters from the ...
