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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Seating Plan for meetings

I really don't know how to describe this but appreciate any help in solving it: We hold a weekly meeting with a variable number of attendees (Currently between 20 & 24) and currently arrange them on 3-4 round tables with 6-8 people per table. We…
Simon Fisher
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Should I divide this permutation problem into cases or are there any quicker methods?

I have got an idea for the second question but I think my approach is too long and I would like to ask whether there are any other quicker methods? Eight cards are selected with replacement from a standard pack of 52 playing cards, with 12 picture…
user71346
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Permutations and Combination rearrangement

I approached this exam question the wrong way apparently, help please? Consider the word "mathematics". In how many ways can you rearrange all the letters so that the vowels are paired and always apart?
Kalena
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Taking square root of cycle permutations

Let $\alpha$ and $\beta$ be permutation cycles of $\{1,2,\ldots,n\}$ such that $\alpha^2=\beta^2$ Can we conclude that $\alpha=\beta$, if (a) $\alpha,\beta$ are odd? (b) $\alpha,\beta$ are even? We can write $\alpha=(a_1 a_2\ldots a_k), \beta=(b_1…
Kunal
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Dividing people into pairs, permutations and combinations

How do we calculate the no of ways of dividing 100 people into 50 pairs?
user34304
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Circular Permutations With Repetitions (Mirrored Ignored)

For Circular Permutations with unique elements (mirrored ignored) the answer is (n - 1)!/2 (pretty straight forward). However I cant seem to figure out how to calculate circular permutations with repetitions allowed. So the Question is: Given 'm'…
GB_echo
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Permutations\Combinations from digits

Using digits 1,2,3,4,5,7 only, how many numbers could be made that are between 2500 and 5000, if a digit is not repeated? (If it had been 2000-5000, that would have been easy!!!) The answer at my level should only use $^nP_{r}$, $^nC_{r}$ and\or…
schooler
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Permutations of letters under some conditions

Let $W(p,q,r,s)$ be the number of permutations of the letters which satisfy the following conditions : Condition 1 : The letters are consist of $P,Q,R,S$. Condition 2 : The number of letter $P,Q,R,S$ is $p,q,r,s$ respectively. Condition 3 : Any two…
mathlove
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Permutations with chess pieces

Let's say we have chess table $n^2$ and we want to put 8 rooks on the table, so that none of them are under eachother's fire. I've come up with this: $$n^2 + n^2(n-1)+n^2(n-1)(n-2) ...$$ I think that I'm not taking into account that the pieces are…
user108078
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Product of non-disjoint k-cycles

I have two $k$-cycles $\alpha=(a \dots c \dots b \dots)$ and $\beta=(a \dots b \dots c \dots)$ and $\alpha \neq \beta^{-1}$. How to show that the product $\alpha \beta$ does not result in a cyclic permutation (just one cycle permutation). Or,…
LuizG
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arrangement of a group of people.

The no. of ways in which 4 particular persons A,B,C,D and 6 other persons can stand in a queue so that A always stands before B, B before C and C before D is ? My try: since A B C D always have to stand together taking them as one, we get, 7! Ans Is…
john
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Permutations Math Practice

In how many permutations of 1,..,n does the integer 1 precede the integer 2? (For instance, (1,3,2), as opposed to (2,3,1)). I am trying to check my answer to this competition practice problem: (n-1)!
computerScientistD
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(Asymptotically?) Minimal set of single-use swaps to generate all permutations

Define $SWAP_n = \{ \sigma \in S_n : \lvert Fix(\sigma) \rvert = n - 2 \}$ For every $n, L \in \mathbb{N}$, and every $G : \{1, ..., L \} \to SWAP_n$, if for every $\tau \in S_n$, there exist $k \le L$, and an increasing function $f_{G, \tau} : \{1,…
Alberto Perrella
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permutation sets

I am interested in the set of all permutations between two sets of the same cardinality. For example, all mappings (6 of them in this case) from (1,2,3) to (5,6,7). Does such a set of permutations have a name or established properties? I am not…
user3433489
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How find total amount of possible permutations

I have an issue that I thought it would be relatively easy to solve, however it has proven to be tougher than originally thought. I have tried to simplify my problem into the following question(s): If I have numbers $1-16$ and these numbers have to…
notmathematician
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