A generalisation of a second partition theorem of Andrews to overpartitions

摘要

In 1968 and 1969, Andrews proved two partition theorems of theRogers-Ramanujan type which generalise Schur's celebrated partition identity(1926). Andrews' two generalisations of Schur's theorem went on to become twoof the most influential results in the theory of partitions, findingapplications in combinatorics, representation theory and quantum algebra. In arecent paper, the author generalised the first of these theorems tooverpartitions, using a new technique which consists in going back and forthbetween $q$-difference equations on generating functions and recurrenceequations on their coefficients. Here, using a similar method, we generalisethe second theorem of Andrews to overpartitions.