A New Approach to Integer Partitions

In this work we define a new set of integer partition, based on a lattice path in Z 2 connecting the line x + y = n to the origin, which is determined by the two-line matrix representation given for different sets of partitions of n . The new partitions have only distinct odd parts with some particular restrictions. This process of getting new partitions, which has been called the Path Procedure , is applied to unrestricted partitions, partitions counted by the 1st and 2nd Rogers–Ramanujan Identities, and those generated by the Mock Theta Function T 1 ∗ ( q ) = ∑ n = 0 ∞ q n ( n + 1 ) ( - q 2 , q 2 ) n ( q , q 2 ) n + 1 .