Elementary properties

Task number: 2456

Determine graphs, cycles, a factorzation into transpositions, the number of inversions, the sign, and the inverse permutations for the following permutations: \(p\), \(q\) and their compositions \(q\circ p\) and \(p\circ q\). (Permutations are composed as mappings, i.e. \((q\circ p)(i)=q(p(i))\).)

  • Variant 1

    \(p=(6{,}4,1{,}5,3{,}2)\), \(q=(6{,}4,3{,}2,5{,}1)\).

  • Variant 2

    \(p=(1{,}2,7{,}6,5{,}4,3{,}8,9)\), \(q=(1{,}3,5{,}7,9{,}8,6{,}4,2)\).

  • Variant 3

    \(p=(5{,}4,3{,}2,1{,}9,8{,}7,6)\), \(q=(8{,}6,4{,}2,1{,}3,5{,}7,9)\).

  • Variant 4

    \(p=(3{,}6,9{,}2,5{,}8,1{,}4,7)\), \(q=(9{,}8,7{,}6,5{,}4,3{,}2,1)\).

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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