Odd and even but not odd and odd or even and even pairs?

Question

I want to know how I can differentiate in plain English these two kinds of pairs:

The first type:

(odd, even)
(even, odd)

which means that the order doesn't matter but two values in a pair should be of different types. And the second type:

(odd, odd)
(even, even)

Which means only when the two values in a pair are of the same type.

How can I name these two type of index in a coordinate system?

Answer 1

Most of the time "non-matching pairs" should be fine. If you want to describe pairs where are the same, you can say "matching pairs". "Heterogeneous pairs" could be used for the ones where they are different too, with "homogeneous pairs" for the ones that are the same as each other.

In either case, clarify what you mean after you use it for the first time, and in the rest of your paper you can use your chosen term without further explanation.