2015/01/29 by Jehanne Dousse, Dousse, Jehanne
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT
paper · pdf · doi:10.48550/arxiv.1501.07478
18 pages. arXiv admin note: substantial text overlap with arXiv:1405.0255
arxiv created 2015/01/29 · openalex publication_date 2015/01/29 · arxiv updated 2015/01/30 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
In 1968 and 1969, Andrews proved two partition theorems of the Rogers-Ramanujan type which generalise Schur's celebrated partition identity (1926). Andrews' two generalisations of Schur's theorem went on to become two of the most influential results in the theory of partitions, finding applications in combinatorics, representation theory and quantum algebra. In a recent paper, the author generalised the first of these theorems to overpartitions, using a new technique which consists in going back and forth between q-difference equations on generating functions and recurrence equations on their coefficients. Here, using a similar method, we generalise the second theorem of Andrews to overpartitions.