A New Approach to Integer Partitions

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In this work we define a new set of integer partition, based on a lattice path in $${\mathbb {Z}}^2$$ 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 $$T_1^*(q)=\sum _{n=0}^{\infty }\dfrac{q^{n(n+1)}(-q^2,q^2)_n}{(q,q^2)_{n+1}}$$ .