1. Thanks for coming.
2. Thanks for your coming.
Which of the above sentences is acceptable?
I've heard people say things like "You can't touch an Englishman without his wanting to".
Why can't people say "Thanks for your coming"?
Is it because it's not complete?
Then how about this one: Thanks for your coming to my apartment.
I don't think the phrase is gramatically incorrect, but it may be just uncommon. Indeed, would you thank a person for somebody else's coming? I guess 'your' is not uttered as it is implied by the person you are talking to.
I may be wrong, though.
I think that it's not a real problem. We can say - Thank you for your answer.
Well, 'answer' is a noun, and it requires a determiner. You can also say "Thank you for the answer". However, you cannot say "Thank you for the coming", because "coming" is a gerund. And I'm inclined to believe that using 'your' would be redundant.
Why do you bring "the" up? We were talking about "your coming" - possessive pronoun + gerund.
Kotfor, I've already explained it.
Thank you for coming.
Thank you for helping me.
"Your" is not needed here because it is implied. You are unlikely to say "thank you for Peter's coming", "thank you for Mike's helping me". We thank the person who has come/helped.
Thank you for your answer.
Thank you for your help.
"Your" here serves as a possessive determiner preceding a noun.
I don't mind coming.
I don't mind your coming.
A personal pronoun makes a difference in sentences like these.
That's how I would explain the whole thing to myself. I am neither a teacher nor a native speaker.
I am not a teacher.
In "thanks for coming", "coming" is not a gerund. In "Thanks for coming to my party", "coming" is a participle heading a phrase. If you shorten that to "thanks for coming", "coming" doesn't turn into a gerund, it remains a participle.