TL;DR: I am wondering if there is a proper mathematical nomenclature for the instances generated by this algorithm (given that there are unique and specific definitions for the words "permutation" and "combination"):
"You are given a sequence of n sets of independently variable size. To generate an "instance," you must select exactly 1 element from each set. Generate all possible instances."
Example given: ( Set A: { 1, 2, 3 }, Set B: { 1, 2 } )
This would produce: (1,1),(2,1),(3,1),(1,2),(2,2),(3,2)
What would these instances be called?
Details:
To make that a bit more concrete, the real-world example that led me to write this algorithm is this: my company is selling 2 flavors of health-conscious ice cream, and on the website's order form for this ice cream, we wanted to provide customers with the option of variable quantities up to a maximum of 6 for each.
So, imagine 2 quantity selectors (1 for vanilla, 1 for chocolate), options ranging 0-6. (In this example, the flavors/selectors are the sets, and the quantities are the objects.)
A customer could choose (0 vanilla x 1 chocolate), (1 vanilla x 1 chocolate), (2 vanilla x 1 chocolate), etc... these would be the "instances" I am trying to name.
We don't care about the number of sets or the cardinality/size of each set (i.e. it doesn't matter how many flavors we have, nor what the maximum quantity for each would be.)
If anyone is curious, here is the program, written in Javascript: https://jsfiddle.net/ybj90vdn/
Cartesian product, ordered pair, tuple, and product type are all words that you might find relevant. Since I don't know what you want to say, I'm not sure which is best for your use cases.