Two-color partitions with evens in one color

TL;DR

This paper studies two-color integer partitions where even parts are restricted to one color, deriving formulas and identities for specific constrained subsequences.

Contribution

It introduces new formulas and identities for two-color partitions with parity and color constraints, expanding understanding of partition enumeration.

Findings

Derived formulas for constrained two-color partitions

Established identities relating to partition enumeration

Analyzed subsequences with parity and color restrictions

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.