= Alexander numbering
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An Alexander numbering assigns an <integer> to each region of an oriented <link diagram> so that crossing an oriented arc from right to left increases the number by one. Normalize the \b[unbounded region to zero]; this fixes the otherwise arbitrary additive constant. Equivalently, the number is the total <winding number> of the projected oriented curves about a point of that region.
In the corresponding <Dehn presentation of a knot group>, a region generator of number $m$ maps under <abelianization> to $t^m$, when each positively oriented <meridian of a knot> maps to $t$. The exterior normalization is necessary: the unbounded-region generator is the identity, so its exponent must be zero. Number differences across adjacent regions recover the meridional exponent one.
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