# Questions tagged [multisets]

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

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### Defining the Set of Rational Numbers

I was wondering about how to define the set of rational numbers, as I am currently learning about set theory in a class of mine. We were going through using set builders to define sets and produced ...
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### How many groups of pentagonal flower bouquets can be formed?

A florist has three types of flowers: tulips, roses, and daisies. There are 4 tulips, 5 roses, and 6 daisies. These 15 flowers are to be arranged into three bouquets of 5 flowers each. Assume that ...
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### Some sum of two elements exceeds a third one in a finite multiset with bounded values

For a multiset $S = \{ a_1,a_2,a_3,\ldots,a_k \}$ where $k = 13$ and $1 \leqslant a < 32$, prove that there exists a subset $s = \{ a_i, a_j, a_k \}$ such that each sum of two elements exceeds the ...
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### How do you translate 'positions of a value 2' into a mathematical notation when defining a bijection?

Let's say I have a multi-set: $(1,1,2)$ And I want to define a bijection from $A$ to $B$ such that: $(1,1,2)$ becomes {3} and, $(1,1,1)$ becomes {} and, $(2,2,2)$ becomes {1,2,3} or, in general, it is ...
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### Find number of ways to divide a set into 2 parts

In how many ways can we divide a set into 2 parts having an element in equal number in both of resulting subsets. For example, multiset = {1, 2, 3, 5, 5, 5, 5} and ...
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### Total number of combinations.

Total number of combination of $a,b,c$ and $d$ where elements can repeat up to maximum $m,n,o,p$ times respectively.(Note: order does not matter , i.e., ${a,b}$ and ${b,a}$ will be count as one only). ...
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### Find elements of $\{0,1\}^4$

For a classroom repartition problem, I need to find a multiset of 8 vectors among $\{0,1\}^4$ such that Multiset: A vector can be present several times in the multiset Their sum with the regular ...
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### Products of multisets tend toward mean

I need some hints on this... So I have multisets (sets where the same value can occur more than once) consisting of nonnegative integers $x$, with $0 \le x < p$. I would like to prove that if I ...
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### Number of arrangements of multiset with different neighbours.

There are $n$ groups of objects with $x_i$ objects from group $i$ ($1 \le i \le n$). Compute the number of ways to arrange them in a line, such that there are no two consecutive objects from one group ...
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### How many 10-combinations from the set $S$ with 5 distinct type $a,b,c,d,$ and $e$?

Problem. Given a multiset $S=\lbrace \infty.a, \infty.b, \infty.c, \infty.d, \infty.e \rbrace$, where $a,b,c,d$ and $e$ are distinct. How many the 10-combinations from $S$ where $a$ and $c$ at least ...
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### What is the mathematical “set” function can be used to represent the uniqueness of a set?

What is the mathematical set function that can satisfy the following if X = (1, 2, 3, 4, 5), Y = (1, 3, 4, 2, 5), Z = (1, 1, 3, 2, 5); Then F(X) = F(Y) ≠ F(Z) what function "F" can be used to ...
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### On day 1, Adam can take 1 walk, on day 2 he can take 2 (so on until day n), how many ways can he take 3 walks?

I'm trying to solve this question, but I'm not quite there and need some help. Question: Adam has just recovered from a serious leg injury and is encouraged to walk to aid his recovery. On day 1, he ...
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### Unable to think about 10-combinations of a multiset

I am trying assignments of an Institute in which I don't study and i could not think about this problem. Problem is -> Determine the number of 10-combinations of multisets S= { 3.a, 4.b, 5.c} I ...
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### Unordered sampling without replacement (inductive proof)

Question: I'm being asked to prove by induction that the size of the sample space equals the multiset equation: $\vert \Omega \vert =(\frac{m+n-1}{n})$ Specific Case There are M total balls ...
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### CSR includes all $h_{ij}$

CSR includes all $h_{ij}$, where i union j includes all members of a set between 1 and n, OR needs to consist of all members of a set that contains multiples of each value in the set. Basically ...
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### Enumeration of multisets satisfying a certain 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 there ...
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### Combinatorics Question about Generating Functions and Multisets

I am faced with the following question from my undergraduate Combinatorics class: There are n aisles in a shop. We want to separate them into consecutive nonempty groups for different categories of ...