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Function invariant under cyclic permutation of arguments

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#permutations #permutation-cycles
39
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solution verification solve the permutation equation

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#abstract-algebra #permutations #solution-verification #permutation-cycles
57
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decompose the permutation $\sigma$ in cycle notation into an object

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970
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In how many ways can a permutation cycle be decomposed as a product of transpositions?

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#group-theory #finite-groups #symmetric-groups #permutation-cycles
108
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Prove using First Isomorphism Theorem

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#group-theory #group-isomorphism #permutation-cycles
52
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Image of an involution under Cayley action in $A_n$

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#group-theory #solution-verification #symmetric-groups #group-actions #permutation-cycles
52
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Show equality about composition of permutations

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#linear-algebra #abstract-algebra #permutations #permutation-cycles
63
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How do we calculate the power of the cycles?

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#abstract-algebra #permutations #permutation-cycles
162
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Given $G:=S_7,M:=\{1,...,7\},g:=(1\, 3\, 6)\cdot(3\, 5),x := 5,$ calculate $g\cdot x$.

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#abstract-algebra #group-theory #permutations #symmetric-groups #permutation-cycles
27
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How do we continue at the inductive step?

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#permutations #induction #permutation-cycles
316
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Number of all cycles in permutations is equal to n!

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#permutations #permutation-cycles
1.2k
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If $\sigma$ is an odd permutation, explain why $\sigma^2$ is even but $\sigma^{-1}$ is odd.

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#combinatorics #group-theory #permutations #permutation-cycles #parity
41
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If $ B^{8}=(234591)$and if $B\in S_{9}$.what is the value of $B$

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#group-theory #permutation-cycles
466
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Summation of signless Stirling numbers of first kind

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#combinatorics #discrete-mathematics #stirling-numbers #permutation-cycles
610
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Find a formula for c(n, n − 2).

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