Combinatorial Proofs for Two-colour Partitions
Year: 2025
Type: article
Abstract: Andrews and El Bachraoui [‘On two-colour partitions with odd smallest part’, Preprint, arXiv:2410.14190] explored many integer partitions in two colours, some of which are generated by the mock theta functions of third order of Ramanujan and Watson. They also posed questions regarding combinatorial proofs for these results. In this paper, we establish bijections to provide a combinatorial proof of one of these results and a companion result. We give analytic proofs of further companion results.
Authors: DANDAN CHEN, ZIYIN ZOU
Institution: Shanghai University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,550
OpenAlex ID: W4409365526