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

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Alternating groups and linear groups

I learned from the literature that the symmetric group $S_n$ can be viewed a subgroup of permutation matrices of $GL_n(q)$ (where $q$ is a prime power), the general linear group of invertible $n\times ... user avatar Steve Stahl

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How many five-character sequences composed of lower case letters and digits be formed if letters may be repeated but digits cannot be repeated?

Permutation/Combination where some elements, such as lower case character of the alphabet a-z are repeating, and some are non-repeating such as number of 0-9, for a string that is 5 characters long. ... user avatar Stefanos

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Doubt on inclusion of members in $S_3$.

Am preparing notes and faced one question as stated below, also request vetting of contents. My main question is stated in the edit below. Order of $S_n$ is given by the set of elements in it. $S_n$ ... user avatar jiten

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If the word “WOW” can be rearranged in exactly 3 ways (WOW, OWW, WWO), how many different arrangements of the letters in “MISSISSIPPI” are possible? [duplicate]

The total number of distinct arrangements which is $\frac{11!}{1!4!4!2!}=34650$ How is this calculated? Is this a binomial coefficient? I don't understand why the denominators are the size of the ... user avatar Germania

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Is the following combinatorial relation correct?

I am confused regarding the following problem in combinatorics ( statistical mechanics ). Suppose I have the following relation : $$\sum_{i=1}^N n_i=\bar{N}$$ I have to find out the number of possible ... user avatar RayPalmer

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Path from leaf to root permutation

Consider a tree in which each vertex has 5 children, and let us label the edges with $a$ or $b$ such that the edges from any parent to its children are always ordered $(a,b,a,b,b)$. See the figure for ... user avatar RedPen

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Probability regarding yellow and white cabs and two independent witnesses

20% of the cabs are white and the other 80% are yellow. A cab was involved in an accident and ran away. An eyewitness to the accident claims that the cab was yellow. Knowing that eyewitness tell the ... user avatar BrownJamba948

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Is any $S_4$-invariant function also $S_6$ invariant?

Consider the following embedding of the permutation group $S_4$ inside $S_6$: $\sigma \in S_4 \to \tilde \sigma \in S_6$, where $$ \tilde \sigma\big(a_{12},a_{13},a_{14},a_{23},a_{24},a_{34}\big)=\big(... user avatar Asaf Shachar

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What is this technique called? Similar to finding all permutations of two arrays.

A paper I was reading referred to the following as interleaving. But that doesn't look quite right. Given two arrays X and Y where the num elements in X: kc, and the num elements in Y:kr. As a short ... user avatar Eric King

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how to list element in cyclic subgroup and notation [closed]

list the elements of the cyclic subgroup <(1 8 2 9 3)(4 5)(6 7)>≤S9 in cycle notation. Is it （45）(67)(1)（12389）（19283）（13928）（18293）right？But the answer has 8 element s? user avatar Bo Peng

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In how many ways can an engineering student select and schedule three technical electives in his final four semesters?

I've the following question: An engineer needs to take three technical electives sometime during his final four semesters. The three are to be selected from a list of ten. In how many ways can he ... user avatar Beta

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If $2$ cyclic permutations have the same cycle length, then they are conjugate

This is the $2^{nd}$ part of a two-part question. The first part asks us to prove that the conjugate of a $j$-cycle $\sigma = (k_1 ... k_j)$ by any other permutation $\tau \in S_n$ is a $j$-cycle and ... user avatar Numerical Disintegration

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Average number of the maximum amount of fixed points of permutation in a partition of $S_n$

Consider the symmetric group $S_n$ and, for each $\sigma \in S_n$, let $f(\sigma)$ be the number of fixed points of $\sigma$. Now let $g$ be the permutation such that $g(i)=i+1$ for $i=1,...,n-1$ and $... user avatar Pedro Vaz Pimenta

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What is the flaw in this approach?

$12$ delegates exists in three cities $C_1,C_2,C_3$ each city having $4$ delegates. A committee of six members is to be formed from these $12$ such that at least one member should be there from each ... user avatar Umesh shankar

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Counting permutations with inclusion-exclusion

How many permutations are there of the letters XXXYYYZZZ if no more than two X’s can appear together and no more than two Y’s can appear together? I get a vague idea that I should use PIE to solve ... user avatar grxxes75

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