The Theorem that Won the War: Activities for Part 2.3 (Cycle Notation)

Jeff Suzuki (Brooklyn College)


  1. Find the cycle decomposition for the given permutations.
    1. \(A =\begin{pmatrix}a    &b    &c    &d    &e    &f\\e    &c    &d    &f    &a    &b\end{pmatrix}\)
    2. \(B =\begin{pmatrix}a    &b    &c    &d    &e    &f\\f    &b    &a    &e    &d    &c\end{pmatrix}\)
    3. \(C =\begin{pmatrix}a    &b    &c    &d    &e    &f\\c    &f    &a    &e    &d    &b\end{pmatrix}\)
  2. Find the cycle decompositions for the Enigma encryptions you found in exercise 3 of Part 2.2 (Conjugates).
  3. Find \(\sigma\tau\) for the given \(\sigma, \tau\).
    1. \(\sigma = (ac)(bf)(de)\), \(\tau = (af)(de)(bc)\)
    2. \(\sigma = (ad)(be)(cf)\), \(\tau = (bf)(de)(ac)\)

Return to the overview of Part 2.3 (Cycle Notation).

Continue to the overview of Part 2.4 (The Message Key).