question  when RC says no notes does that include books signed by the author? sometime 

they say thank you or enjoy the book

[i always wonder about this]

If the RC says "no notes", then, to my mind, that would include a note from the author.  Otherwise they'd say "no writing except for an author signature or note."

Yes, with a RC worded like that, I would make sure the book has no writing at all.

I agree with Patty, although in my mind I consider "notes" to be of two varieties. First , are notes or annotations within the text of the book and, second, are notes that are inscriptions from a gift giver or an author.

Books with notes or writing within text pages are not swappable here except in cases of textbooks, workbooks or travel guides in which case the sender must PM the requestor about the writing and both parties agree to the transaction before the book is sent.

Books with inscriptions fall into a borderline gray area. Specifically, does an inscription count as a "note" whether on the fly leaf, inside the front cover, or on the title page?

Here is an excerpt from the Help Docs

• a signature or note on the flyleaf or inside front or back cover is OKAY
• an author's signature on the title page is OKAY

See Book Condition Criteria for 'Swappability' at PBS for the full text of the doc.

Personally, inscriptions from an author are OK with me, although I much prefer them when they are generic; i.e., when the author does not include a personal name in the inscription. The Help Doc cited above, however, references an "author's signature", not an "author's signature with inscription", so I would interpret an RC specifying "no notes" as meaning no inscriptions at all, not even from the author.

No one can answer that except the person who wrote the RC. It doesn't sound like you are asking about a specific case, but a "in theory" question.

I personally would interpret "no notes" as a "no messages written and no margin notes" and an author signature with nothing but their name I would not consider a note and would tell the requester that exact opinion if I got a RWAP on the transaction (IMO, they would need to say No Writing if they didn't want anything at all including a basic signature, notes means...a note, a message, something more than a signature).