Mathematics Stack Exchange
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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this can be solved bypermutation and combination based problem

How many three are there whose hundred digit is greater than tens digit which in turn is greater than the unit digit? Ans:I tried it But couldn't solve..
shashi
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How many legal permutations are there of D&D ability score results?

In Dungeons and Dragons 3.5 edition, ability score generation results in 6 values, each of which is between 3 and 18 (inclusive). They can repeat. Each score is accompanied by an ability score modifier, which is equal to 0.5*(ability score-10),…
Tim S
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Does *every* permutation commute with *some* transposition?

I'm getting started with the study of permutations on $n$ objects, and I'm trying to prove/disprove something that is probably trivial: does every permutation commute with some transposition?
user750041
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Permutations in Rows; Garden Optimization Problem

Imagine a small garden, divided into 8 equal parts, each a square foot. The garden is 4 ft x 2 ft, so the "bins" are in two rows. Let's number them as: 0 1 2 3 4 5 6 7 Now, each of these plants has other plants that they like, that's good for them…
dev3827
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Permutation and combinations prob

there are $k$ different things and the task is to arrange them at $n$ places such that no adjacent things are of the same type and first and last things are of the same type. An example for: $k=3,n=4$ 1 , 2 ,3 ,1 2 ,3 ,1 ,2 3 ,1 ,2 ,3 so on as one…
Avaneesh Kumar
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How to solve this problem about composition of permutations?

If i have this arrangement $(1,2,..,k,...,n)$. $\sigma$ is a permutation of the $n$ elements and $\rho$ is a permutation of the first $k\leq n$ elements. How i can show that the following set: $$\{\sigma \circ \rho \hspace{0.1cm} | \text{$\sigma,…
sango
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Finding the sum of numbers formed by digits

I know how to find the sum of all numbers formed by digits 1,2,3,4,5 taken all at a time without repetitions. How can I find the sum when digit repetitions are allowed?
anik bhowmick
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possible $n$ letter combinations in a $k$ by $k$ table of letters

If I have a table which has $k$ columns and $k$ rows (same number of rows and columns) that contains letters of the English alphabet, what are the number of $n$ letter combinations I can create from this table while $n \le k$? Letters can be chosen…
M.P
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What is inverse number in permutation?

I came across inverse number defined as - the number of transpositions of pairs of elements that must be composed to place the elements in canonical order $012\ldots(n-1)$. Please clarify it with an example. In general is there any way to calculate…
Adam Levine
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Odd permutations example

How to prove that this permutation: p=(1,10,9,7,6)(2,8,4)(3,5) is odd. Thanks much!
ABCD
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Can we swap items in a list an odd number of times without changing it?

Suppose there is a list with finitely many distinct items. In each move we swap two of them. How to show that it is impossible to make moves odd times and make the list back to the original state? (Or is it actually possible?)
user
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cycle type of product of permutations.

Let $\sigma$ and $\tau$ be two permutations in $S_n$ with partitions $\lambda$ and $\mu$ as their cycle type. What is the cycle type of the product $\sigma \tau$ in terms of $\lambda$ and $\mu$? Thank you.
GA316
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Permutation and combination with males/females

There are $6$ males and $6$ females in the finals of a talent competition. A contest is held to pick the top $3$ winners in both the male and female categories in order of merit. How many different entries must be completed to ensure a winning…
yasmine
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How many permutations are there of all the letters of the word PATHFINDER with restrictions...

How many permutations are there of all the letters of the word PATHFINDER with the following restrictions: 1) no vowels together, 2) all vowels together. I know there are 10! ways to arrange 10 different letters. Not sure how to address the…
Armando W
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Find the numbers greater than 23000 that can be formed from the digits 1,2,3,5,6 without repeating any digits

So, I do understand the concept of permutations, but I can't figure out how the formula for finding permutations even applies to this. The author solves it as follows, but he does not make any explicit comments as to why he did what he…
Arkilo
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