Counting Restricted Integer Partitions


Blair, David Dakota, "Counting Restricted Integer Partitions" (2015). CUNY Academic Works.

Polynomials for m up to 23.


Let p_b(n) be the number of integer partitions of n whose parts are powers of b. For each m there is a generating function identity: f_m(b,q)\sum_{n} p_b(n) q^n = (1-q)^m \sum_{n} p_b(b^m n q)q^n where n ranges over all integer values. This dataset is a JSON object with keys m from 1 to 23 whose values are f_m(b,q). This file is also published as Polynomials occuring in generating function identities for b-ary partitions at CUNY Academic Works.