[jakebol]

Just to note that language "duplicates in sparse arrays" doesn't make sense, if you allow for duplicates it is no longer an array by definition.

[DaiPlusPlus]

Arrays (vectors) can have duplicates - don’t you mean a set?

[evanpw]

I think the duplicates are in the coordinate dimension, like x[1] having more than one value, rather than x[1] and x[2] have the same value.