One-way syncing for Linux

One-way sync scenario–Folder F of computer A is one-way synced with folder FC of computer C (the “cloud”):

  1. All changes in folder F are automatically replicated in FC, including deleted files. (Nice-to-have option at this point: delete file from F without deleting from FC. (Deleted F files to be renamed to something else in FC.))
  2. All changes to files in FC that originate from F and have the same names as their F counterparts to be automatically replicated in F.
  3. Any files in FC that do not come from F (or originate from F files but were deleted from F–see “nice-to-have option” above), to be excluded from syncing.