Two-color partitions with evens in one color

Abstract

We consider sequences counting integer partitions in two colors (red and blue) in which the even parts occur only in blue color. We focus on subsequences defined by constraints on the parity and color of the summands. We establish formulas for our sequences and deduce identities of integer partitions.

10 pages, LaTeX. Corrected missing minus signs in Theorems 1 and 2, the corresponding proof lines, and the resulting statements of Corollaries 1 and 2. Results otherwise unchanged