<Dd> <Table> <Tr> <Td> </Td> </Tr> </Table> </Dd> <Table> <Tr> <Td> </Td> </Tr> </Table> <P> The Durfee square has applications within combinatorics in the proofs of various partition identities . It also has some practical significance in the form of the h - index . </P> <P> There is a natural partial order on partitions given by inclusion of Young diagrams . This partially ordered set is known as Young's lattice . The lattice was originally defined in the context of representation theory, where it is used to describe of the irreducible representations of symmetric groups S for all n, together with their branching properties, in characteristic zero . It also has received significant study for its purely combinatorial properties; notably, it is the motivating example of a differential poset . </P>

Formula for number of partitions of an integer