Genitive with Ellipsis

The genitive case is one of the 4 main cases in modern English.  Whilst it has other uses (explained below), it is predominantly the form used to indicate possession.  For nouns, it is usually created by adding 's to the word or by preceding it with "of".Examples: Carl's haircut the edge of the table

When the genitive case is used to show possession, it may also be classified as the "possessive case".  

Example:

Dan's bike (genitive case and possessive case)

However, the genitive case does not always indicate possession.Examples: children's songs (genitive case)(In this example, the children do not own the songs.  They are songs for children.) Constable's paintings (genitive case)(Constable may not own the paintings. This denotes only that they are paintings by Constable.)

This is a combination of the prepositional and the inflected genitive. It usually has a partitive meaning:

A work of Milton’s (one of Milton’s works)

A friend of his father’s.