Mathematical formalisation of transposition ciphers

Formally:

• For block length $t$, let $\mathcal{K}$ be the set of permutations on $\{1,\dots ,t\}$. For each $e\in \mathcal{K}$ and $m\in \mathcal{M}$: $$E_e(m)=m_{e(1)}{m}_{e(2)}\dots m_{e(t)}$$
• The set of all such transformations is called a transposition cipher.
• To decrypt $c=c_1{c}_2\dots c_t$ compute $D_d(c)=c_{d(1)}{c}_{d(2)}\dots c_{d(t)}$, where $d$ is inverse permutation.
• Letters unchanged so one can exploit frequency analysis for dipthongs, tripthongs, words, etc.