fall is a common carpet tack

used to refer to the season chiefly in the USA - autumn in Regency Period Britain and still in use.

gotten is a particularly sharp and frequently encountered carpet tack.

 Linguistically well known for being in common usage in the USA, but less well known for its utter decline in the UK. That decline occurred prior to the Regency period.

The compilers of the database for the Austen Thesaurus at Write Like Jane Austen input every word use by Jane Austen in her books. 'gotten' does not exist in either the text or the conversations. Check it out.