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15
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Simplification of permutation $(1 2 3 4) (4 5 6 7)$

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#group-theory #permutations #permutation-cycles
75
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Solve $\sigma^2=(1345)(2687)$ in $S_8$

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#abstract-algebra #group-theory #permutations #permutation-cycles
68
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**trajectories** of the permutation of $S_6$ , $\sigma = (1 2 356) (345)$

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#group-theory #permutations #permutation-cycles
62
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Working in $S_6$ compute $(134) \cdot (12).$

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#group-theory #permutations #symmetric-groups #permutation-cycles
204
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Are the conjugacy classes normal subgroups in $S_n$?

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#group-theory #normal-subgroups #permutation-cycles
414
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Prove $a(n, k) = t(n, k + 1)$ with permutations and cycles where 1 and 2 are/are not in the same cycle?

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#combinatorics #generating-functions #permutation-cycles
188
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How to sort a permutation cycle in the mapping form?

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#mathematica #permutation-cycles #sorting
252
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Prove that a symmetric group $S_n$ has a cyclic subgroup of order $n$.

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#abstract-algebra #group-theory #symmetric-groups #cyclic-groups #permutation-cycles
66
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Equivalent ways of representing a cycle

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#abstract-algebra #group-theory #permutations #solution-verification #permutation-cycles
87
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How to express a cycle decomposition of $c^d$?

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#group-theory #permutation-cycles
318
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Find the number of permutations $\sigma \in S_n$ with exactly $c_i$ cycles of length $i$ for each $i$.

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#sequences-and-series #combinatorics #permutation-cycles
76
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Product of signs of two juxtaposition of two disjoint permutations

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#combinatorics #discrete-mathematics #permutations #permutation-cycles
36
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Is the function $f(x,y)$ describing the given graph is symmetric for any $x\neq y$? Or, only for $x=y$?

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#permutations #symmetry #permutation-cycles #symmetric-functions
221
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Product formula for sign of permutation

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#permutations #symmetric-groups #permutation-cycles
357
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Let $\sigma, \tau \in S_n$. Prove $\sigma\tau \text{ is even} \iff \sigma \text{ and }\tau$ are both even or both odd.

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#abstract-algebra #group-theory #solution-verification #symmetric-groups #permutation-cycles

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