In 1969, Andrews proved a theorem on partitions with difference conditions
which generalises Schur's celebrated partition identity. In this paper, we
generalise Andrews' theorem to overpartitions. The proof uses q-differential
equations and recurrences

Dousse, Jehanne

English

arXiv

Abstract. 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 appli-cations in combinatorics, representation theory and quantum algebra. In a recent paper, the author generalised the first of these theorems to overparti-tions, 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. 1

Jehanne Dousse

CiteSeerX

A GENERALISATION OF A SECOND PARTITION THEOREM OF ANDREWS TO OVERPARTITIONS

Abstract. In 1969, Andrews [3] proved a theorem on partitions with dif-ference conditions which generalises Schur’s celebrated partition identity. In this paper, we generalise Andrews ’ theorem to overpartitions. Our proof uses q-difference equations and recurrences. 1

A GENERALISATION OF A PARTITION THEOREM OF ANDREWS

http://www.liafa.univ-paris-diderot.fr/%7Ejdousse/andrews%20large.pdf

A generalisation of a partition theorem of Andrews to overpartitions

Abstract

Similar works

Full text

Available Versions

CiteSeerX

CiteSeerX