List questions from permutation-cycles

Published on 24 Oct 2022 - 13:58

750

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Proof that there are $n!/2$ even permutations of [n]

Published on 25 Oct 2022 - 20:51

103

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Bracelet enumeration

Published on 27 Mar 2026 - 2:16

271

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What is the maximum value of $\sum_{i=1}^{n} \vert \sigma(i) - i \vert, $ where $\ \sigma\ $ is a permutation of $\ [n]\ ?$

Published on 10 Nov 2022 - 21:48

244

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Let $\alpha$ belong to $S_n$. Prove that $|\alpha|$ divides $n!$

Published on 16 Nov 2022 - 3:59

42

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Composition of two cube rotation symmetries, that lie along perpendicular axis.

Published on 25 Mar 2026 - 7:48

41

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Understanding how to get composition of disjoint cycles from composition of nondisjoint cycles in a proof

Published on 24 Nov 2022 - 17:40

198

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Prove that this sum equals 0

Published on 27 Nov 2022 - 0:41

134

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$S_4$ as a subgroup of $GL_3(\mathbb{F}_2)$

Published on 26 Mar 2026 - 12:40

49

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Can you find these sets of permutations?

Published on 26 Mar 2026 - 16:05

106

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Finding an unknown permutation when given the product with a known permutation.

Published on 04 Dec 2022 - 23:23

43

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Number of permutations $\sigma\in S_5$ such that $\sigma^{12}={\rm id}$?

Published on 06 Dec 2022 - 8:43

85

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Find a permutation $X \in S_6$ which satisfies the equation

Published on 26 Mar 2026 - 17:31

74

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Computing the coefficients of the egf of derangements

Published on 24 Feb 2026 - 3:31

39

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An equivalent condition for a subset is not a block under a group action

Published on 19 Dec 2022 - 13:58

List Question

Transform permutation into another permutation with minimum swaps and/or moves

Proof that there are $n!/2$ even permutations of [n]

Bracelet enumeration

What is the maximum value of $\sum_{i=1}^{n} \vert \sigma(i) - i \vert, $ where $\ \sigma\ $ is a permutation of $\ [n]\ ?$

Let $\alpha$ belong to $S_n$. Prove that $|\alpha|$ divides $n!$

Composition of two cube rotation symmetries, that lie along perpendicular axis.

Understanding how to get composition of disjoint cycles from composition of nondisjoint cycles in a proof

Prove that this sum equals 0

$S_4$ as a subgroup of $GL_3(\mathbb{F}_2)$

Can you find these sets of permutations?

Finding an unknown permutation when given the product with a known permutation.

Number of permutations $\sigma\in S_5$ such that $\sigma^{12}={\rm id}$?

Find a permutation $X \in S_6$ which satisfies the equation

Computing the coefficients of the egf of derangements

An equivalent condition for a subset is not a block under a group action

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