Combinatorial Proofs of Some Results of Andrews and El Bachraoui

2024/10/21 by Mahanta, Pankaj Jyoti, Saikia, Manjil P.
#05A17 #11P81 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.15852

Abstract

Recently, Andrews and El Bachraoui (2024) proved three very interesting q-series identities, from which three simple looking identities involving certain restricted partitions into distinct even parts and 4-regular partitions follow. In this short note, we give combinatorial proofs of these identities. We also prove the counterpart identities for the restricted partitions into distinct odd parts.

Related

• Combinatorial proof of identities involving partitions with distinct even parts and 4-regular partitions
• The combinatorics of identities involving overpartitions with distinct parts
• Combinatorial Extensions on Andrews and El Bachraoui's Almost-Distinct Partitions
• Identities involving partitions with distinct odd parts and no parts congruent to 2 mod 4
• Combinatorial proofs of several partition identities of Andrews and Merca