= Glaisher partition bijection
{c}
Fix a prime $p$. Replace each part $p^a m$, with $p\nmid m$, by $p^a$ copies of $m$. This is a size-preserving bijection from <regular partitions> to <partitions of an integer> whose parts are not divisible by $p$. To invert it, write each multiplicity of a part $m$ not divisible by $p$ in base $p$ and use its digit in position $a$ as the multiplicity of $p^a m$. Every resulting multiplicity is below $p$. The bijection explains why the number of simple symmetric-group <modules> equals the number of <p-regular elements>' <conjugacy classes>.
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