the empty name vs an empty name

It doesn't have to be; you could write 'an empty string'
but they are perhaps thinking of the empty string as a constant that you could give a name to if you wished, which is fine too.
d

Understood! Thank you!

MUSCOVITECould you please explain why the definite article (not the indefinite one) is used before "empty string" in this example sentence?

I'd say it's because there is only one of them, conceptually. Similarly in mathematics, the null set.

CJ

Thanks, CalifJim!

Looks like either article can be used with the following word combinations?

You can use a/the for all three but I wouldn't state that their use is entirely free to choose from.

You gave the example
"i.e. if the name is the/an empty string"

however you have to have
i.e. if the name is (a) null" --- 'a' is optional
it cannot be "the" null here.

d

MUSCOVITELooks like either article can be used with the following word combinations?

I suppose so, but the math books I'm familiar with use "the".

MUSCOVITEThere should be more similar word combinations (in math and elsewhere)?

There may be, but I can't think of any right now.

CJ

Thanks everybody for their input!