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Mathematics Stack Exchange

Questions tagged [permutations]

For questions related to permutations, which can be viewed as re-ordering a collection of objects.

The word permutation has several possible meanings, based on context. In combinatorics, a permutation is generally taken to be a sequence containing every element from a finite set exactly once. Permutations of a finite set can be thought of as exactly the ways in which the elements of the set can be ordered.

In group theory, a permutation of a (not necessarily finite) set $S$ is a bijection $\sigma : S \to S$. The set of all permutations of $S$ forms a group under composition, called the symmetric group on $S$.

Reference: Permutation.

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how to statistically infer a causal relationship between different variables and an outcome

background We are running an operation using the variables in the following table to result in an outcome under the ATC success rate % column: (note: this table is only a sample.. the number of permutations can be very large, ie (number of…
abbood
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how to get the number of permutations from a finite list

I'm trying to get the number of permutations from a table that looks like this: is it (number of providers) * (number of machine categories) * (proxy providers) * (proxy subnets) * (websites)?
abbood
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How to find the number of ways to arrange $6$ men in a row such that $3$ particular men are consecutive

Find the number of ways to arrange $6$ men in a row such that $3$ particular men are consecutive. Now first I have to select those $3$ men which can be done in $C(6,3)$ ways. How do I proceed? Thanks
J. Deff
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How many times must this transformation be repeated to return to the initial state?

In the 15-puzzle, suppose the initial state (on the left) is transformed by legal moves to the state on the right in the diagram below. How many times must this transformation be repeated to return to the initial state? I'm really uncertain how to…
mathstack
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Showing that the set of odd permutations is not a subgroup of Sn

I want to show that the set of odd permutations is not a subgroup of Sn. Let the set $H= \{\text{odd permutations}\}$. Is it enough to say that the Identity permutation which sends all of its elements on themselves is even therefore, $e \notin H$…
Sylvester Stallone
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Is $f\colon\mathbb Z_{26}\to\mathbb Z_{26}$ a permutation? $f(a)=11a \pmod{26}$

Is $f\colon\mathbb Z_{26}\to\mathbb Z_{26}$ a permutation? $$f(a)=11a\pmod{26}$$ Note: it must be one-to-one and onto. I'm really struggling with how to start this question. Any help would be greatly appreciated!
user384325
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Permutations and combinations for software output

I created a software program that uses the information from Stats Canada Crime data and searches through the crime data file to organize and parse the information. My program asks the user which two provinces they want to compare, which crime they…
kash
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Functions and their Distinct Variants

Here's a question I've been working on: For which of the values of $n$ and $k$ does there exist a function of $n$ variables that has $k$ distinct variants? For example, when $n = 2$ and $k = 1$, I claim that there does exist a function and I chose…
John W. Smith
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Composition of Transpositions Proof

Here is the question that I'm working on: Show that if $n \geq 2$, then every permutation of $\{1,2,...,n\}$ can be expressed as the composition of transpositions of the form ($1$ $a$), where $a = 2,3,...,n$. We'll, let's say that we call such a…
John W. Smith
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Distinct Variants

I'm really having some trouble on this problem: Find the number of distinct variants that the functions have. I'm working with the following function (technically an expression) $$x_1x_2x_3^2$$ From what I read, a variant is basically another way…
John W. Smith
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Permutation and Combination-number divisible by 3

Five digit number divisible by $3$ is formed using $0,1,2,3,4,6$ and $7$ without repetition. Total number of such numbers are?: $(1)312$ $(2)3125$ $(3)120$ $(4)216$ My answer is coming out to be $504$. I don't know where I am going wrong. Please…
Shammy
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Let $\tau=(12\cdots n)\in S_n$ and $\sigma\in S_n$. Prove that $\sigma\tau=\tau\sigma\iff\sigma=\tau^i$

Let $\tau=(12\cdots n)\in S_n$ and $\sigma\in S_n$. Prove that $\sigma\tau=\tau\sigma\iff\sigma=\tau^i$ for some $i\in\{1,\dots,n-1\}$. I can show the $"\impliedby"$ direction. However, I'm struggling with the other one. Say $\sigma\tau=\tau\sigma$.…
Sha Vuklia
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How many ways can 4 children with their mothers be seated in a column such that a child placed always in front of his mother?

How many ways can 4 children with their mothers be seated in a column such that a child placed always in front of his mother? The answer in the book is $$\frac{8!}{2!2!2!2!}$$ I didn't understand how to get this answer, please help me.
user373141
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Larger numbers that can be formed by adding segments to displayed digits

The digits from 0-9 can form other digits by adding segments (as in an electronic display (7 segment display)). So: From 0 you can form: 8; From 1 you can form: 0,3,4,7,8,9; From 2 you can form: 8; From 3 you can form: 8,9; From 4 you can form:…
Chor May
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What does this form mean in terms of permutations?

Say you have a permutation $f$, and you want to know the smallest $m$ such that $f^m$ is the identity, how would you go about this? I'm assuming I have to square, cube etc, but is there a quicker method?
SFL
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