document.write( "Question 1205502: Express each of the following permutations of [ 1 2 3 4 5 6 7 8 ] as a product of transpositions.
\n" ); document.write( "1. [1 2 3 4 3 4 5 6 5 6 8 2 7 8 7 1 ]
\n" ); document.write( "2. [1 2 1 3 3 4 8 4 5 6 6 7 7 8 5 2 ]
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Algebra.Com's Answer #847956 by CPhill(1959)\"\" \"About 
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To express a permutation as a product of transpositions, we need to identify the pairs of elements that need to be swapped to transform the identity permutation into the given permutation.\r
\n" ); document.write( "\n" ); document.write( "**1. [1 2 3 4 3 4 5 6 5 6 8 2 7 8 7 1 ]**\r
\n" ); document.write( "\n" ); document.write( "We can break down this permutation into the following steps:\r
\n" ); document.write( "\n" ); document.write( "1. Swap 2 and 8: (2 8)
\n" ); document.write( "2. Swap 1 and 7: (1 7)
\n" ); document.write( "3. Swap 3 and 4: (3 4)
\n" ); document.write( "4. Swap 5 and 6: (5 6)\r
\n" ); document.write( "\n" ); document.write( "So, the permutation can be expressed as a product of transpositions:\r
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\n" ); document.write( "(2 8)(1 7)(3 4)(5 6)
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\n" ); document.write( "\n" ); document.write( "**2. [1 2 1 3 3 4 8 4 5 6 6 7 7 8 5 2 ]**\r
\n" ); document.write( "\n" ); document.write( "We can break down this permutation into the following steps:\r
\n" ); document.write( "\n" ); document.write( "1. Swap 2 and 3: (2 3)
\n" ); document.write( "2. Swap 4 and 8: (4 8)
\n" ); document.write( "3. Swap 6 and 7: (6 7)
\n" ); document.write( "4. Swap 5 and 2: (5 2)\r
\n" ); document.write( "\n" ); document.write( "So, the permutation can be expressed as a product of transpositions:\r
\n" ); document.write( "\n" ); document.write( "```
\n" ); document.write( "(5 2)(6 7)(4 8)(2 3)
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