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«A cycle is a product of transpositions» $\iff$ «Rearrangement of $n$ objects is the same as successively interchanging pairs»

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#group-theory #permutations #function-and-relation-composition #permutation-cycles
124
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Clarification needed regarding why identity can be written only as a product of even number of 2-cycles

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#abstract-algebra #permutations #permutation-cycles
1k
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Multiplication in permutation Group- cyclic

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#abstract-algebra #permutations #permutation-cycles
248
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Rules for multiplying non-disjunctive permutation cycles

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#permutations #permutation-cycles
490
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Find number of square permutations

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#permutations #permutation-cycles
256
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Non-unique representation of permutations.

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#abstract-algebra #permutations #permutation-cycles
590
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Why write permutations as disjoint cycles and transpositions?

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#abstract-algebra #permutations #permutation-cycles
75
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Permutations with no common symbols

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#permutations #permutation-cycles
382
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Number of ways of build a binary matrix with constraints

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#combinatorics #permutations #combinations #permutation-cycles
1.2k
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How to show that $\mathbb{Z}_{12} $ is isomorphic to a subgroup of $S_7$?

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#group-theory #permutation-cycles
118
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Special subsets of Symmetric group $S_n$ from Barrington's theorem

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#abstract-algebra #group-theory #permutations #symmetric-groups #permutation-cycles
94
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How to solve $\beta^{-1}\pi^{2016}\beta = \alpha$ where $\alpha$, $\beta$ are given permutations

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#discrete-mathematics #permutations #cyclic-decomposition #permutation-cycles
683
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When do two permutations commute?

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#abstract-algebra #group-theory #permutations #permutation-cycles
50
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Commutativity of cycles in decomposition of commutative permutations

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#permutations #permutation-cycles
52
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Unable to correctly get order of permutation.

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#abstract-algebra #permutation-cycles

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