If I type thank you, I can't post it. So it is better not to say thank you? Thank you is up voting the answer?
Yes. If the answer was helpful to you, up-voting is the correct action to take. There has been a LOT of discussion across the Stack Exchange network about what "superfluous elements" are permitted in questions and answers. The consensus is that we prefer just information in questions, rather than pleasantries. My personal favorite explanation of the "say no to thank-you" is Jon Skeet's view. Also, look at point 3 from TXI's answer.
If you want to tell the answerer something specific about how the answer helped in a comment, that's fine. But comments that are basically "+1!" or "Wow, thanks, that's awesome!" don't really add value to the questions and answers.
That being said, if you meet an answer author in real life or on one of the Stack Exchange chats, there's nothing at all wrong with stopping to say "Thank you!"