Mathematical definition of mono-alphabetic substitution ciphers

• Let $\mathcal{K}$ be the set of all permutations of the alphabet $\mathcal{A}$. Define for each $e\in \mathcal{K}$ an encryption transformation $E_e$ on strings $m=m_1{m}_2\dots m_n\in \mathcal{M}$ as $E_e(m)=e(m_1)e(m_2)\dots e(m_n)=c_1{c}_2\dots c_n=c$
• To decrypt $c$, compute the inverse permutation $d=e^{-1}$ and $D_d(c)=d(c_1)d(c_2)\dots d(c_n)=m$
• $E_e$ is a mono-alphabetic substitution cipher