How do the narrator and liberty 5-3000 begin their communication? What earlier relationship does this echo

He learns her name as she is called back to the fields by the others, and he begins to look forward to seeing her every day, although he knows that he is forbidden to express preference for one woman. One day, Liberty 5-3000 also turns to look at him with her taut, severe face before walking away. The next day, Liberty 5-3000 smiles at him, and they begin to greet each other every morning at the hedge between the road and the fields. They do so silently, with a subtle salute, because neither of them is allowed to communicate with those of other vocations. I think he also felt a preference for International 4-8818 but for different reasons.