The combinatorics of some two-color partition identities

2025/10/29 by Shen, Yong-Chao
#Algebraic combinatorics #Combinatorics (math.CO) #FOS: Mathematics #G.2.1

paper · doi:10.48550/arxiv.2510.25104

Abstract

Recently, Andrews and EI Bachraoui obtained several iden tities on two-colored partitions. While solving open problems they posed, Chen and Zhou derived a number of identities using analytic methods and asked for combinatorial proofs. In this note, we provide the requested combinatorial proofs. Additionally, we derive several new identities and provide combinatorial proofs for them.

Citations

• Combinatorial Proofs for Overpartitions and Two-Colored Partitions II
• Two-color partitions and overpartitions: a combinatorial proof
• Positive Weighted Partitions Generated by Double Series
• Rank, two-color partitions and Mock theta function
• On two-color partitions with odd smallest part
• Combinatorial proofs and refinements of three partition theorems of Andrews

Cited by

• Two-color partitions and overpartitions: a combinatorial proof

Related

• Two-color partitions and overpartitions: a combinatorial proof
• Combinatorial Proofs for Overpartitions and Two-Colored Partitions II
• Combinatorial proofs and refinements of three partition theorems of Andrews
• Combinatorial Proofs for Two-Color Partition Identities Involving Overpartitions and Minimal Excludants
• 2-colored Rogers-Ramanujan partition identities